Alternative Pseudodifferential Analysis

With an Application to Modular Forms

  • André Unterberger

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. André Unterberger
    Pages 1-9
  3. André Unterberger
    Pages 11-26
  4. André Unterberger
    Pages 75-91
  5. 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.


Pseudodifferential analysis Rankin-Cohen brackets Representation theory anaplectic representation calculus

Authors and affiliations

  • André Unterberger
    • 1
  1. 1.Mathématiques Université de ReimsReims Cedex 2France

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