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Alternative Pseudodifferential Analysis [electronic resource] : With an Application to Modular Forms / by André Unterberger.

By: Unterberger, André [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextTextSeries: Lecture Notes in Mathematics: 1935Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008Description: IX, 118 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540779117.Subject(s): Differential equations, partial | Topological Groups | Fourier analysis | Number theory | Partial Differential Equations | Topological Groups, Lie Groups | Fourier Analysis | Number TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.353 Online resources: Click here to access online
Contents:
Preface -- Introduction -- The Metaplectic and Anaplectic Representations -- The One-dimensional Alternative Pseudodifferential Analysis -- From Anaplectic Analysis to Usual Analysis -- Pseudodifferential Analysis and Modular Forms -- Index -- Bibliography.
In: Springer eBooksSummary: 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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Preface -- Introduction -- The Metaplectic and Anaplectic Representations -- The One-dimensional Alternative Pseudodifferential Analysis -- From Anaplectic Analysis to Usual Analysis -- Pseudodifferential Analysis and Modular Forms -- Index -- Bibliography.

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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