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Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1935)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
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
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Mathématiques Université de Reims, Reims Cedex 2, France
André Unterberger
Bibliographic Information
Book Title: Alternative Pseudodifferential Analysis
Book Subtitle: With an Application to Modular Forms
Authors: André Unterberger
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-77911-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-77910-0Published: 03 September 2008
eBook ISBN: 978-3-540-77911-7Published: 14 November 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 118
Topics: Differential Equations, Topological Groups and Lie Groups, Fourier Analysis, Number Theory