Alternative Pseudodifferential Analysis

With an Application to Modular Forms

By: AndrÃ© Unterberger

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Paperback | 3 September 2008

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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.

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Introduction	p. 1
The Metaplectic and Anaplectic Representations	p. 11
The Metaplectic Representation	p. 11
Anaplectic Analysis	p. 16
The One-Dimensional Alternative Pseuodifferential Analysis	p. 27
Ascending Pseudodifferential Analysis	p. 28
Classes of Operators	p. 38
The Resolvent of the Lowering Operator	p. 57
The Composition Formula	p. 64
From Anaplectic Analysis to Usual Analysis	p. 75
The v-Anaplectic Representation	p. 75
Ascending Pseudodifferential Calculus in v-Anaplectic Analysis	p. 83
Pseudodifferential Analysis and Modular Forms	p. 93
The Eisenstein, Theta, Poincare, and Alternative Poincare Distributions	p. 93
Moyal Brackets and Rankin-Cohen Brackets	p. 106
References	p. 115
Index	p. 117
Subject Index	p. 118
Table of Contents provided by Ingram. All Rights Reserved.

Alternative Pseudodifferential Analysis

With an Application to Modular Forms

At a Glance

Paperback

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