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  • Book
  • © 2008

Alternative Pseudodifferential Analysis

With an Application to Modular Forms

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1935)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
  2. Introduction

    • André Unterberger
    Pages 1-9
  3. The Metaplectic and Anaplectic Representations

    • André Unterberger
    Pages 11-26
  4. From Anaplectic Analysis to Usual Analysis

    • André Unterberger
    Pages 75-91
  5. Pseudodifferential Analysis and Modular Forms

    • André Unterberger
    Pages 93-114
  6. Back Matter

    Pages 115-122

About this book

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.

Keywords

  • Pseudodifferential analysis
  • Rankin-Cohen brackets
  • Representation theory
  • anaplectic representation
  • calculus
  • partial differential equations

Authors and Affiliations

  • Mathématiques Université de Reims, Reims Cedex 2, France

    André Unterberger

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions