000 03181nam a22005055i 4500
001 978-3-540-46210-1
003 DE-He213
005 20190213151705.0
007 cr nn 008mamaa
008 121227s1989 gw | s |||| 0|eng d
020 _a9783540462101
_9978-3-540-46210-1
024 7 _a10.1007/BFb0093683
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aReiter, Hans.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMetaplectic Groups and Segal Algebras
_h[electronic resource] /
_cby Hans Reiter.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1989.
300 _aXIV, 134 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1382
505 0 _aPreliminaries 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.
520 _aThese 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 Schwartz-Bruhat 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.
650 0 _aTopological Groups.
650 0 _aNumber theory.
650 1 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662192009
776 0 8 _iPrinted edition:
_z9783540514176
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1382
856 4 0 _uhttps://doi.org/10.1007/BFb0093683
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11552
_d11552