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Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52135176339729,"sku":"NLS9783764385132","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764385132.jpg?v=1789558287"},{"product_id":"pseudodifferential-operators-with-automorphic-symbols-book-andr-unterberger-9783319186566","title":"Pseudodifferential Operators with Automorphic Symbols","description":"The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144972136721,"sku":"NLS9783319186566","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319186566.jpg?v=1786045878"},{"product_id":"pricing-derivatives-under-levy-models-book-andrey-itkin-9781493967902","title":"Pricing Derivatives Under Levy Models","description":"\u003cp\u003eThis monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThe latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eWritten for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. 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Consider on the line the distributions m (12) ? d (x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation,orundermultiplicationbythefunctionx ? e , the?rst(resp. second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th (resp. 8th) root of unity. Then, consider the metaplectic representation Met, 2 a unitary representation in L (R) of the metaplectic group G, the twofold cover of the group G = SL(2,R), the de?nition of which will be recalled in Section 2: it extends as a representation in the spaceS (R) of tempered distributions. From what has just been said, if g ˜ is a point of G lying above g? G,andif d = d even g ˜ ?1 or d , the distribution d =Met(g˜ )d only depends on the class of g in the odd homogeneousspace?\\G=SL(2,Z)\\G,uptomultiplicationbysomephasefactor, by which we mean any complex number of absolute value 1 depending only on g ˜. 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For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed.\u003cbr\u003ePseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied.\u003cbr\u003eAn introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and \u003ci\u003eC\u003c\/i\u003e*-algebras.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52667569963281,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52667570880785,"sku":"NLS9783031283970","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031283970.jpg?v=1762282882"},{"product_id":"symplectic-methods-in-harmonic-analysis-and-in-mathematical-physics-book-maurice-a-de-gosson-9783764399917","title":"Symplectic Methods in Harmonic Analysis and in Mathematical Physics","description":"The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52677429690641,"sku":"NLS9783764399917","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764399917.jpg?v=1786050936"},{"product_id":"localization-problem-in-index-theory-of-elliptic-operators-book-vladimir-nazaikinskii-9783034805094","title":"The Localization Problem in Index Theory of Elliptic Operators","description":"The book deals with the localization approach to the index problem for elliptic operators. 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