Alternative Pseudodifferential Analysis: With an Application to Modular Forms, Issue 1935

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Springer Science & Business Media, Sep 3, 2008 - Mathematics - 118 pages
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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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Contents

Introduction
1
The Metaplectic and Anaplectic Representations
11
22 Anaplectic Analysis
16
The OneDimensional Alternative Pseudodifferential Analysis
27
31 Ascending Pseudodifferential Analysis
28
32 Classes of Operators
38
33 The Resolvent of the Lowering Operator
57
34 The Composition Formula
64
From Anaplectic Analysis to Usual Analysis
75
42 Ascending Pseudodifferential Calculus in vAnaplectic Analysis
83
Pseudodifferential Analysis and Modular Forms
93
52 Moyal Brackets and RankinCohen Brackets
106
References
115
Index
117
Subject Index
118
Copyright

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