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Progress in Mathematics

By: AndrÃ© Unterberger

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Hardcover | 11 December 2002

At a Glance

Hardcover
260 Pages

Dimensions(cm)
23.5 x 15.88 x 1.91

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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 R²invariant 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.

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Foreword	p. 1
Introduction	p. 3
Automorphic Distributions and the Weyl Calculus
The Weyl calculus, the upper half-plane, and automorphic distributions	p. 11
Eisenstein distributions, Dirac's comb and Bezout's distributions	p. 18
The structure of automorphic distributions	p. 28
The main formula: a heuristic approach	p. 40
A Higher-level Weyl Calculus of Operators
A tamer version of the Weyl calculus: the horocyclic calculus	p. 53
The higher-level metaplectic representations	p. 59
The radial parts of relativistic wave operators	p. 74
The higher-level Weyl calculi	p. 82
Can one compose two automorphic operators?	p. 95
The sharp product of two power-functions: the Weyl case	p. 106
Beyond the symplectic group	p. 118
The Sharp Composition of Automorphic Distributions
The Roelcke-Selberg expansion of functions associated with [actual symbol not reproducible]: the continuous part	p. 131
The Roelcke-Selberg expansion of functions associated with [actual symbol not reproducible]: the discrete part	p. 151
A proof of the main formula	p. 163
Towards the completion of the multiplication table	p. 171
Further Perspectives
Another way to compose Weyl symbols	p. 195
Odd automorphic distributions and modular forms of non-zero weight	p. 217
New perspectives and problems in quantization theory	p. 228
Index of Notation	p. 239
Subject Index	p. 241
Bibliography	p. 243
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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The Physics Book

Big Ideas Simply Explained

Physics for Beginners

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