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In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49738565026065,"sku":"NGR9783642310898","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52666362495249,"sku":"NLS9783642310898","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642310893.jpg?v=1750967425"},{"product_id":"introduction-to-analytic-number-theory-book-komaravolu-chandrasekharan-9783642461262","title":"Introduction to Analytic Number Theory","description":"This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub­ lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. 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Before describing the content of the book in detail, we describe each concept briefly. More extensive introductory descriptions of each concept are in the introductions and notes to Chapters 2, 3 and 4. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. In that sense, a topos is a generalized set theory. However, it originated with Grothendieck and Giraud as an abstraction of the of the category of sheaves of sets on a topological space. Later, properties Lawvere and Tierney introduced a more general id~a which they called \"elementary topos\" (because their axioms did not quantify over sets), and they and other mathematicians developed the idea that a theory in the sense of mathematical logic can be regarded as a topos, perhaps after a process of completion. The concept of triple originated (under the name \"standard construc- in Godement's book on sheaf theory for the purpose of computing tions\") sheaf cohomology. Then Peter Huber discovered that triples capture much of the information of adjoint pairs. Later Linton discovered that triples gave an equivalent approach to Lawverc's theory of equational theories (or rather the infinite generalizations of that theory). Finally, triples have turned out to be a very important tool for deriving various properties of toposes.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50134121906449,"sku":"CIN0387961151G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387961151.jpg?v=1750975311"},{"product_id":"algebraic-operads-book-jean-louis-loday-9783642303616","title":"Algebraic Operads","description":"In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included.   After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50290327879953,"sku":"GOR013914496","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51062747201809,"sku":"NIN9783642303616","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52662642180369,"sku":"NLS9783642303616","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642303617.jpg?v=1750730426"},{"product_id":"nonlinear-analysis-on-manifolds-monge-ampere-equations-book-thierry-aubin-9780387907048","title":"Nonlinear Analysis on Manifolds. 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One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. 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Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma- thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener- ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50404136845585,"sku":"CIN3540150668G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540150668.jpg?v=1750999634"},{"product_id":"basic-number-theory-book-andre-weil-9783540586555","title":"Basic Number Theory","description":"at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes.","brand":"WoB","offers":[{"title":"US \/ WELL_READ \/ SBYB","offer_id":50404265525521,"sku":"CIN3540586555A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":51480920523025,"sku":"CIN3540586555G","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52332539740433,"sku":"NLS9783540586555","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52748359106833,"sku":"NIN9783540586555","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":53489541447953,"sku":"GOR008797479","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540586555.jpg?v=1754286926"},{"product_id":"gauge-field-theory-and-complex-geometry-book-s-merkulov-9783540613787","title":"Gauge Field Theory and Complex Geometry","description":"From the reviews: \"... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field\" (Contemporary Physics )\"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding\" (New Zealand Math. Soc. Newsletter) \" The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!\" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. 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Much new material appears in this second edition, including: dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50933012955409,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":50933013053713,"sku":"NGR9783642084423","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52475733213457,"sku":"NLS9783642084423","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642084427.jpg?v=1751159055"},{"product_id":"algebraic-complexity-theory-book-t-lickteig-9783540605829","title":"Algebraic Complexity Theory","description":"The algorithmic solution of problems has always been one of the major concerns of mathematics. 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Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under­ standing of the intrinsic computational difficulty of problems.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50996773093649,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":50996773945617,"sku":"NIN9783540605829","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52148673642769,"sku":"NLS9783540605829","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540605827.jpg?v=1750730733"},{"product_id":"coherent-analytic-sheaves-book-h-grauert-9783642695841","title":"Coherent Analytic Sheaves","description":"...Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. \"La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'\" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C. R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The \"Monogene analytische Functionen\", which K. WEIERSTRASS glued together from \"Func- tionselemente durch analytische Fortsetzung\", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the \"ideaux de domaines indetermines\", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E. N. S.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50996801405201,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":50996801667345,"sku":"NIN9783642695841","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52655753494801,"sku":"NLS9783642695841","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642695841.jpg?v=1751159084"},{"product_id":"geometry-of-algebraic-curves-book-enrico-arbarello-9780387909974","title":"Geometry of Algebraic Curves","description":"In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre­ sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli­ cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51001994019089,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51001997197585,"sku":"NIN9780387909974","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52483842834705,"sku":"NLS9780387909974","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387909974.jpg?v=1751038795"},{"product_id":"arithmetic-functions-and-integer-products-book-pdta-elliott-9781461385509","title":"Arithmetic Functions and Integer Products","description":"Every positive integer m has a product representation of the form where v, k and the ni are positive integers, and each Ei = ± I. A value can be given for v which is uniform in the m. A representation can be computed so that no ni exceeds a certain fixed power of 2m, and the number k of terms needed does not exceed a fixed power of log 2m. Consider next the collection of finite probability spaces whose associated measures assume only rational values. Let hex) be a real-valued function which measures the information in an event, depending only upon the probability x with which that event occurs. Assuming hex) to be non­ negative, and to satisfy certain standard properties, it must have the form -A(x log x + (I - x) 10g(I -x». Except for a renormalization this is the well-known function of Shannon. What do these results have in common? They both apply the theory of arithmetic functions. The two widest classes of arithmetic functions are the real-valued additive and the complex-valued multiplicative functions. Beginning in the thirties of this century, the work of Erdos, Kac, Kubilius, Turan and others gave a discipline to the study of the general value distribution of arithmetic func­ tions by the introduction of ideas, methods and results from the theory of Probability. I gave an account of the resulting extensive and still developing branch of Number Theory in volumes 239\/240 of this series, under the title Probabilistic Number Theory.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51027552141585,"sku":"NIN9781461385509","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52618464657681,"sku":"NLS9781461385509","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1461385504.jpg?v=1751116027"},{"product_id":"arrangements-of-hyperplanes-book-peter-orlik-9783540552598","title":"Arrangements of Hyperplanes","description":"An arrangement of hyperplanes is a finite collection of codimension one     affine subspaces in a finite dimensional vector space. Arrangements have    emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces,                        representation theory, reflection groups, singularity theory, and           in computer science and physics. This book is the first comprehensive   study of the subject. It treats arrangements with methods from              combinatorics, algebra, algebraic geometry, topology, and group actions.    It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the        foundations of the theory. Consequently, it is essentially self-contained   and proofs are provided. Nevertheless, there are several new                results here. In particular, many theorems that were previously known   only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into      a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems,  and a comprehensive bibliography of the subject.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061019869457,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061022458129,"sku":"NIN9783540552598","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52142993899793,"sku":"NLS9783540552598","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540552596.jpg?v=1750870546"},{"product_id":"theorie-der-steinschen-raume-book-h-grauert-9783642666506","title":"Theorie der Steinschen Raume","description":"1. Der klassische Satz von Mittag-LeIDer, nach dem in jedem Gebiete der GauB- schen Zahlenebene ce meromorphe Funktionen mit vorgegebenen Hauptteilen konstruiert werden konnen, wurde bereits 1895 von P. Cousin auf den Fall von mehreren komplexen Veranderlichen iibertragen. Allerdings konnten Cousin und nachfolgende Autoren den analogen Satz nur fUr spezielle Gebiete, namlich Zylindergebiete des m-dimensionalen komplexen Zahlenraumes cern, beweisen. m Es zeigte sich, daB keineswegs in allen Gebieten des ce, 2 S; m","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061126365457,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061129117969,"sku":"NIN9783642666506","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52655850258705,"sku":"NLS9783642666506","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642666507.jpg?v=1750902949"},{"product_id":"group-theory-ii-book-m-suzuki-9783642868870","title":"Group Theory II","description":"This is a translation from the Japanese of the second volume (chapters four through six) of my book \"Gunron\" (Iwanami Shoten, 1978). After discussing the concept of commutators in the fourth chapter, we tum to a discussion of the methods and theorems pertaining to finite groups. The last chapter is intended as an introduction to the recent progress in the theory of simple groups. Forihe translation, I have kept the main body of the text unchanged, however I have added a few comments in the last chapter in order to inform the readers of the most recent progress. I would like to express my appreciation to Kazuko Suzuki for her devoted help in translating this book. Finally, it gives me great pleasure to acknowl­ edge my indebtedness to my wife, Naoko, for her constant support and understanding, and for converting the long and often illegible manuscript into a beautifully typed one. To her, I express my sincere thanks and appreciation. July, 1985 Michio Suzuki Contents (Part II) List of Notation IX Chapter 4 Commutators § 1. Commutator Subgroups §2. Nilpotent Groups 13 37 §3. Commutator Calculations 54 §4. 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The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061468823825,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061471707409,"sku":"NIN9783540547532","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52135581090065,"sku":"NLS9783540547532","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540547533.jpg?v=1750967735"},{"product_id":"lectures-on-closed-geodesics-book-w-klingenberg-9783540083931","title":"Lectures on Closed Geodesics","description":"The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo­ metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres­ ponding periodic orbit in the geodesic flow is infinitesimally stable.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062654763281,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062657876241,"sku":"NIN9783540083931","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52128712851729,"sku":"NLS9783540083931","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540083936.jpg?v=1750773949"},{"product_id":"fourier-analysis-and-nonlinear-partial-differential-equations-book-hajer-bahouri-9783642168291","title":"Fourier Analysis and Nonlinear Partial Differential Equations","description":"In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. 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Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological\/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source.   The first volume appeared 1985 as vol. 267 of the same series.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51062852747537,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51062856581393,"sku":"NIN9783662506202","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52592036872465,"sku":"NLS9783662506202","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":53025293828369,"sku":"NGR9783662506202","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3662506203.jpg?v=1751383244"},{"product_id":"isometric-theory-of-classical-banach-spaces-book-he-lacey-9783642657641","title":"The Isometric Theory of Classical Banach Spaces","description":"The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1 \u0026lt; p \u0026lt; 00, then it is well known that X=L (j1,IR) where 1\/p+1\/q=1 and if p=oo, then X=L (v,lR) for q j some measure v. Thus, the only case where a space is obtained which is not truly classical is when p = 1. This class of spaces is known as L - 1 predual spaces since their duals are L type. It includes some well known j subclasses such as spaces of the type C(T, IR) for T a compact Hausdorff space and abstract M spaces. The structure theorems concern necessary and sufficient conditions that a general Banach space is linearly isometric to a classical Banach space. 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New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51063227580689,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51063230791953,"sku":"NIN9783662517451","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52589769130257,"sku":"NLS9783662517451","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3662517450.jpg?v=1750773556"},{"product_id":"interpolation-spaces-book-j-bergh-9783642664533","title":"Interpolation Spaces","description":"The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu­ script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. 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Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research...\" Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064458248465,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51064460968209,"sku":"NIN9783540643258","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51892496630033,"sku":"GOR006789272","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52423718699281,"sku":"NLS9783540643258","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540643257.jpg?v=1751032192"},{"product_id":"convex-analysis-and-minimization-algorithms-i-book-jean-baptiste-hiriart-urruty-9783540568506","title":"Convex Analysis and Minimization Algorithms I","description":"Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. 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Such integrations frequently involve (not always in immediately re­ cognizable form) elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems. As a result, he may entirely avoid problems which lead to elliptic integrals, or is likely to resort to graphical methods or other means of approximation in dealing with all but the simplest of these integrals. It became apparent in the course of my work in theoretical aero­ dynamics that there was a need for a handbook embodying in convenient form a comprehensive table of elliptic integrals together with auxiliary formulas and numerical tables of values. 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By \"non-homogeneous boundary value problem\" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space\" on m\" and the G\/ s spaces\" on am\" ; j we seek u in a function space u\/t \"on m\" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as \"working hypothesis\" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U\/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u\/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a \"natural\" way with problem (1), (2) and con­ j venient for applications, and also all possible choiees for u\/t and {F; G} j in these families.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064835080465,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51064837603601,"sku":"NIN9783642651632","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52622595555601,"sku":"NLS9783642651632","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3642651631.jpg?v=1750774637"},{"product_id":"sobolev-spaces-book-vladimir-maz-ya-9783642155635","title":"Sobolev Spaces","description":"Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. 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Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems. Bull. L.M.S. 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At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. 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The author discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class field theory is . particularly rich in illustrating complements, hints for further study, and concrete examples. The concluding chapter VI on zeta-functions and L-series is another outstanding advantage of the present textbook. The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available. W. Kleinert in Z.blatt f. Math., 1992 The author's enthusiasm for this topic is rarely as evident for the reader as in this book. - A good book, a beautiful book. F. Lorenz in Jber. DMV 1995 The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. 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Aber nicht minder ist meine Dberzeugung (was ich nie unter- lassen babe, hinzuzuftigen), daB ein solcher Unterricht, entsprechend der heutigen Entwickelung der Wissenschaft, ftir die Ausbildung der Fachmathematiker auf der Oberstufe nicht gentigt, daB hier vielmehr neben den Tatsachen der Anschauung die zentrale Bedeutung des modernen Zahlbegriffs und der weitgehenden mit ihm zusammen- hangenden Entwickelungen hervortreten muB. Und nun vermisse ich in den Lehrbtichern und Vorlesungen, welche ich kenne, die Uber- leitung von der einen Auffassung zur anderen. Hier will sich die fol- gende Darstellung als eine Erganzung einschieben; ihr bestes Ziel wird erreicht sein, wenn sie sich eines Tages als tiberfliissig erweisen sollte, weil die Uberlegungen, die sie bringt, zu selbstverstandlichen Bestand- teilen jedes hoheren mathematischen Unterrichts geworden sind. Gottingen, den 28. Februar 1902. F. Klein. Vorwort zur zweiten Auflage. Das Folgende ist im wesentlichen ein unveranderter Abdruck der ersten Ausgabe dieser Vorlesungen vom Jahre 1902. Nur an einzelnen Stellen sind einige Ungenauigkeiten verbessert, sowie in gelegentlichen Zusatzen Hinweise auf neuere Publikationen gegeben, die in engstem Zusammen- hange mit den in der Vorlesung gegebenen Entwickelungen stehen. Am Schlusse ist ein Abdruck des, Gutachtens der Gottinger philosophischen Fakultat betreffend die Beneke-Preisaufgabe ftir 1901, auf das die Aus- ftihrungen des Textes verschiedentlich Bezug nehmen, hinzugeftigt. Gottingen, den 5. Januar 1907. C. H. Miiller. Vorwort zur dritten Auflage. Die Vorlesung F.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52125035561233,"sku":"NLS9783540041283","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52761652330769,"sku":"NIN9783540041283","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540041283.jpg?v=1757461413"}],"url":"https:\/\/www.worldofbooks.com\/collections\/grundlehren-der-mathematischen-wissenschaften-book-series.oembed?page=7","provider":"World of Books ","version":"1.0","type":"link"}