Metaplectic Groups and Segal Algebras [electronic resource] / by Hans Reiter.
 Publication:
 Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.
 Format/Description:
 Book
1 online resource (XIV, 134 pages)  Series:
 Lecture Notes in Mathematics, 00758434 ; 1382
Lecture Notes in Mathematics, 00758434 ; 1382  Contained In:
 Springer eBooks
 Online:
 Connect to full text
http://hdl.library.upenn.edu/1017.12/2328961  Status/Location:

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Details
 Subjects:
 Topological Groups.
Number theory.  Local subjects:
 Topological Groups, Lie Groups. (search)
Number Theory. (search)  System Details:
 text file PDF
 Summary:
 These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A. Weil's theory of metaplectic groups. It is shown that Weil's main theorem holds for a class of functions (a certain Segal algebra) larger than that of the SchwartzBruhat functions considered by Weil. The theorem is derived here from some general results about this class which seems to be a rather natural one in the context of Weil's theory. No previous knowledge of the latter is assumed, however, and the theory is developed here, step by step; Further, a complete discussion of the Segal algebra concerned is given, with references to the literature. Weil's metaplectic groups are somewhat easier to investigate when the characteristic is not 2; the case of characteristic 2 presents some special features which are fully discussed. New problems that arise are indicated.
 Contents:
 Preliminaries from harmonic analysis and group theory
Segal algebras; the Segal algebra G 1 (G)
Weil's unitary operators and the Segal algebra G 1 (G)
Weil's group of operators and related groups
Vector spaces and quadratic forms ever local fields
Properties of certain quadratic forms
Weil operators for vector spaces over local fields
The metaplectic group (local case); Segal continuity
The metaplectic group and Segal continuity in the adelic case
Weil's theorem 6.  Contributor:
 SpringerLink (Online service)
 Other format:
 Printed edition:
Printed edition:  ISBN:
 9783540462101
 Publisher Number:
 10.1007/BFb0093683 doi
 Access Restriction:
 Restricted for use by site license.