{"title":"Andr Unterberger","description":null,"products":[{"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":"quantization-and-non-holomorphic-modular-forms-book-andr-unterberger-9783540678618","title":"Quantization and Non-holomorphic Modular Forms","description":"This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action of SL(2,Z).","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52414599528721,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52414600282385,"sku":"NLS9783540678618","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540678618.jpg?v=1786791804"},{"product_id":"automorphic-pseudodifferential-analysis-and-higher-level-weyl-calculi-book-andr-unterberger-9783764369095","title":"Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi","description":"Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002. The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2,Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus. Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52428891619601,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52428892406033,"sku":"NLS9783764369095","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764369095.jpg?v=1759165481"},{"product_id":"automorphic-pseudodifferential-analysis-and-higher-level-weyl-calculi-book-andr-unterberger-9783034896412","title":"Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi","description":"Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002. The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2,Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus. Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52430949351697,"sku":"NLS9783034896412","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034896412.jpg?v=1759171107"},{"product_id":"pseudodifferential-methods-in-number-theory-book-andr-unterberger-9783319927060","title":"Pseudodifferential Methods in Number Theory","description":"Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52534567665937,"sku":"NLS9783319927060","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319927060.jpg?v=1787047299"},{"product_id":"fourfold-way-in-real-analysis-book-andr-unterberger-9783764375447","title":"The Fourfold Way in Real Analysis","description":"The One-dimensional Anaplectic Representation.- The n-dimensional Anaplectic Analysis.- Towards the Anaplectic Symbolic Calculi.- The One-dimensional Case Revisited.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52565258993937,"sku":"NLS9783764375447","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764375447.jpg?v=1760741986"},{"product_id":"alternative-pseudodifferential-analysis-book-andr-unterberger-9783540779100","title":"Alternative Pseudodifferential Analysis","description":"\u003cp\u003eThis volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis.\u003c\/p\u003e\n\u003cp\u003eBesides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one. \u003cbr\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52585228894481,"sku":"NLS9783540779100","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540779100.jpg?v=1785979102"},{"product_id":"quantization-and-arithmetic-book-andr-unterberger-9783764387907","title":"Quantization and Arithmetic","description":"(12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. 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 ˜. On the other hand, a function u?S(R) is perfectly characterized by its scalar g ˜ productsagainstthedistributionsd ,sinceonehasforsomeappropriateconstants C , C the identities 0 1 g ˜ 2 2 | d ,u | dg = C u if u is even, 2 0 even L (R) ?\\G","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52660664860945,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52660665745681,"sku":"NLS9783764387907","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764387907.jpg?v=1790165939"},{"product_id":"pseudodifferential-analysis-automorphic-distributions-in-the-plane-and-modular-f-book-andr-unterberger-9783034801652","title":"Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms","description":"Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane   to automorphic distribution theory in the plane.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52679008059665,"sku":"NLS9783034801652","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034801652.jpg?v=1786086657"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-andr-unterberger.oembed","provider":"World of Books ","version":"1.0","type":"link"}