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 208 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.
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.
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.
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 175 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.
Download or read book Handbook of Analytic Operator Theory written by Kehe Zhu and published by CRC Press. This book was released on 2019-05-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analytic Operator Theory thoroughly covers the subject of holomorphic function spaces and operators acting on them. The spaces covered include Bergman spaces, Hardy spaces, Fock spaces and the Drury-Averson space. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators. The volume consists of eleven articles in the general area of analytic function spaces and operators on them. Each contributor focuses on one particular topic, for example, operator theory on the Drury-Aversson space, and presents the material in the form of a survey paper which contains all the major results in the area and includes all relevant references. The overalp between this volume and existing books in the area is minimal. The material on two-variable weighted shifts by Curto, the Drury-Averson space by Fang and Xia, the Cowen-Douglas class by Misra, and operator theory on the bi-disk by Yang has never appeared in book form before. Features: The editor of the handbook is a widely known and published researcher on this topic The handbook's contributors are a who's=who of top researchers in the area The first contributed volume on these diverse topics
Download or read book Partial Differential Equations VIII written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.
Download or read book Quantization and Non holomorphic Modular Forms written by André Unterberger and published by Springer. This book was released on 2007-05-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
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 307 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.
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 459 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.
Download or read book Symmetry in Mathematics and Physics written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2009-07-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume mainly grew out of talks given at a Conference held at UCLA in January 2008, which honored V. S. Varadarajan on his 70th birthday. The main theme of the Conference was symmetry in mathematics and physics, areas of mathematics and mathematical physics in which Varadarajan has made significant contributions during the past 50 years. Very early in his career he also worked and made significant contributions in the areas of probability and the foundations of quantum mechanics. Topics covered by the articles in this volume are probability, quantum mechanics, symmetry (broadly interpreted in mathematics and physics), finite and infinite dimensional Lie groups and Lie algebras and their representations, super Lie groups and supergeometry (relatively new but active and important fields at the interface between mathematics and physics), and supersymmetry. The latter topic takes on a special importance since one of the first experiments at the Large Hadron Collider at CERN will be a test of whether supersymmetry exists in the world of elementary particles. A reprint of an exposition of supersymmetry by one of its founders, B. Zumino, appears in this volume.
Download or read book Journal of analysis and its application written by and published by . This book was released on 2004 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pseudodifferential Operators and Wavelets over Real and p adic Fields written by Nguyen Minh Chuong and published by Springer. This book was released on 2018-11-28 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear degenerate pseudodifferential boundary value problems (BVPs), non-classical pseudodifferential BVPs, wavelets and Hardy spaces, wavelet integral operators, and wavelet solutions to Cauchy problems over the real field and the p-adic field.
Download or read book Journal of Nonlinear Mathematical Physics written by and published by atlantis press. This book was released on with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Alternative Pseudodifferential Analysis written by André Unterberger and published by Springer Science & Business Media. This book was released on 2008-09-03 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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. Besides 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.
Download or read book Symmetries and Laplacians written by David Gurarie and published by Courier Corporation. This book was released on 2007-12-21 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.
Download or read book Number Theory and Modular Forms written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.
Download or read book Mathematical Aspects of Quantization written by Sam Evens and published by American Mathematical Soc.. This book was released on 2012 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.
