Alternative pseudodifferential analysis: With an application to modular forms

André Unterberger (auth.)3540779108, 9783540779100

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.

Table of contents :
Front Matter….Pages i-ix
Introduction….Pages 1-9
The Metaplectic and Anaplectic Representations….Pages 11-26
The One-Dimensional Alternative Pseudodifferential Analysis….Pages 27-74
From Anaplectic Analysis to Usual Analysis….Pages 75-91
Pseudodifferential Analysis and Modular Forms….Pages 93-114
Back Matter….Pages 115-122