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Pseudodifferential Operators With Automorphic Symbols
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Book Synopsis Pseudodifferential Operators with Automorphic Symbols by : André Unterberger
Download or read book Pseudodifferential Operators with Automorphic Symbols written by André Unterberger and published by Birkhäuser. This book was released on 2015-06-22 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Trends in Toeplitz and Pseudodifferential Operators by : Roland V. Duduchava
Download or read book Recent Trends in Toeplitz and Pseudodifferential Operators written by Roland V. Duduchava and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.
Book Synopsis Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi by : André Unterberger
Download or read book Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi written by André Unterberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Algebras, Toeplitz Operators and Related Topics by : Wolfram Bauer
Download or read book Operator Algebras, Toeplitz Operators and Related Topics written by Wolfram Bauer and published by Springer Nature. This book was released on 2020-09-01 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.
Book Synopsis Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms by : André Unterberger
Download or read book Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms written by André Unterberger and published by Springer Science & Business Media. This book was released on 2011-08-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g E SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.
Book Synopsis Pseudodifferential Methods in Number Theory by : André Unterberger
Download or read book Pseudodifferential Methods in Number Theory written by André Unterberger and published by Birkhäuser. This book was released on 2018-07-16 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.
Book Synopsis An Introduction to Pseudo-Differential Operators by : M W Wong
Download or read book An Introduction to Pseudo-Differential Operators written by M W Wong and published by World Scientific Publishing Company. This book was released on 2014-03-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn). The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
Book Synopsis Recent Trends in Toeplitz and Pseudodifferential Operators by : Roland V. Duduchava
Download or read book Recent Trends in Toeplitz and Pseudodifferential Operators written by Roland V. Duduchava and published by Birkhäuser. This book was released on 2013-11-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.
Book Synopsis Pseudodifferential Operators and Spectral Theory by : M.A. Shubin
Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.
Book Synopsis Recent Trends in Toeplitz and Pseudodifferential Operators by : Roland V. Duduchava
Download or read book Recent Trends in Toeplitz and Pseudodifferential Operators written by Roland V. Duduchava and published by Birkhäuser. This book was released on 2010-06-22 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.
Book Synopsis Solvable Algebras of Pseudodifferential Operators by : Boris Plamenevskii
Download or read book Solvable Algebras of Pseudodifferential Operators written by Boris Plamenevskii and published by Springer Nature. This book was released on 2023-05-04 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. 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. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.
Author :I͡Uriĭ Vladimirovich Egorov Publisher :Springer Science & Business Media ISBN 13 :9783764354848 Total Pages :376 pages Book Rating :4.3/5 (548 download)
Book Synopsis Pseudo-Differential Operators, Singularities, Applications by : I͡Uriĭ Vladimirovich Egorov
Download or read book Pseudo-Differential Operators, Singularities, Applications written by I͡Uriĭ Vladimirovich Egorov and published by Springer Science & Business Media. This book was released on 1997 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Introduction to the Theory of Pseudodifferential Operators by : Xavier Saint Raymond
Download or read book Elementary Introduction to the Theory of Pseudodifferential Operators written by Xavier Saint Raymond and published by CRC Press. This book was released on 1991-09-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.
Book Synopsis Introduction To Pseudo-differential Operators, An (2nd Edition) by : Man-wah Wong
Download or read book Introduction To Pseudo-differential Operators, An (2nd Edition) written by Man-wah Wong and published by World Scientific Publishing Company. This book was released on 1999-04-29 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new edition of An Introduction to Pseudo-Differential Operators, the style and scope of the original book are retained. A chapter on the interchange of order of differentiation and integration is added at the beginning to make the book more self-contained, and a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded and an index is added.
Book Synopsis Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms by : YoungJu Choie
Download or read book Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms written by YoungJu Choie and published by Springer Nature. This book was released on 2019-11-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience. The book is intended for researchers and graduate students in number theory.
Book Synopsis Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains by : Harold Widom
Download or read book Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains written by Harold Widom and published by Springer. This book was released on 2006-11-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Trends in Pseudo-Differential Operators by : Joachim Toft
Download or read book Modern Trends in Pseudo-Differential Operators written by Joachim Toft and published by Springer Science & Business Media. This book was released on 2007-01-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ISAAC Group in Pseudo-Differential Operators (IGPDO) met at the Fifth ISAAC Congress held at Università di Catania in Italy in July, 2005. This volume consists of papers based on lectures given at the special session on pseudodifferential operators and invited papers that bear on the themes of IGPDO. Nineteen peer-reviewed papers represent modern trends in pseudo-differential operators. Diverse topics related to pseudo-differential operators are covered.
