{"title":"Im Gel'fand","description":null,"products":[{"product_id":"generalized-functions-volume-4-book-im-gel-fand-9781470426620","title":"Generalized Functions, Volume 4","description":"The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.  The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces $E \\subset H \\subset E'$, where $H$ is a Hilbert space, $E'$ is dual to $E$, and inclusions $E\\subset H$ and $H\\subset E'$ are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51430338199825,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51430338527505,"sku":"GOR014272899","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470426625.jpg?v=1763474541"},{"product_id":"generalized-functions-volume-1-book-im-gel-fand-9781470426583","title":"Generalized Functions, Volume 1","description":"The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.  Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51430338265361,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51430338593041,"sku":"GOR014272897","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470426587.jpg?v=1750923122"},{"product_id":"generalized-functions-volume-2-book-im-gel-fand-9781470426590","title":"Generalized Functions, Volume 2","description":"The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.  Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley-Wiener theorem.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51430338298129,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51430338560273,"sku":"GOR014272898","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470426595.jpg?v=1763484780"},{"product_id":"gelfand-mathematical-seminars-1996-1999-book-im-gel-fand-9780817640132","title":"The Gelfand Mathematical Seminars 1996-1999","description":"Dedicated to the memory of Chih-Han Sah, this volume covers a number of topics, including: combinatorial geometry, connections between logic and geometry, Lie groups, algebras and their representations, and non-communcative algebra and its relations to physics.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52433709924625,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52433710678289,"sku":"NLS9780817640132","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817640132.jpg?v=1759178816"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-im-gel-fand.oembed","provider":"World of Books ","version":"1.0","type":"link"}