Automorphic Pseudodifferential Analysis And Higher Level Weyl Calculi

DOWNLOAD

Download Automorphic Pseudodifferential Analysis And Higher Level Weyl Calculi PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Automorphic Pseudodifferential Analysis And Higher Level Weyl Calculi book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Automorphic Pseudodifferential Analysis And Higher Level Weyl Calculi

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Automorphic Pseudodifferential Analysis And Higher Level Weyl Calculi written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Pseudodifferential Analysis Automorphic Distributions In The Plane And Modular Forms

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-06

Pseudodifferential Analysis Automorphic Distributions In The Plane And Modular Forms written by André Unterberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-06 with Mathematics categories.

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.

Pseudodifferential Operators With Automorphic Symbols

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2015-06-22

Pseudodifferential Operators With Automorphic Symbols written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-22 with Mathematics categories.

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.

Alternative Pseudodifferential Analysis

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Springer
Release Date : 2008-11-14

Alternative Pseudodifferential Analysis written by André Unterberger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-14 with Mathematics categories.

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.

Pseudodifferential Methods In Number Theory

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Birkhäuser
Release Date : 2018-07-16

Pseudodifferential Methods In Number Theory written by André Unterberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-16 with Mathematics categories.

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.

Operator Algebras Toeplitz Operators And Related Topics

DOWNLOAD
Author : Wolfram Bauer
language : en
Publisher: Springer Nature
Release Date : 2020-09-01

Operator Algebras Toeplitz Operators And Related Topics written by Wolfram Bauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.

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.

Symplectic Geometry And Quantum Mechanics

DOWNLOAD
Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-06

Symplectic Geometry And Quantum Mechanics written by Maurice A. de Gosson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-06 with Mathematics categories.

This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

Quantization And Arithmetic

DOWNLOAD
Author : André Unterberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-28

Quantization And Arithmetic written by André Unterberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-28 with Mathematics categories.

(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

Coxeter Matroids

DOWNLOAD
Author : Alexandre V. Borovik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Coxeter Matroids written by Alexandre V. Borovik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

Casimir Force Casimir Operators And The Riemann Hypothesis

DOWNLOAD
Author : Gerrit Dijk
language : en
Publisher: Walter de Gruyter
Release Date : 2010-10-19

Casimir Force Casimir Operators And The Riemann Hypothesis written by Gerrit Dijk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with Mathematics categories.

This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.