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LEADER: 02861nam a22004335a 4500
001 013856822-7
005 20131206204503.0
008 121227s1987 gw | s ||0| 0|eng d
020 $a9783540477624
020 $a9783540477624
020 $a9783540176961
024 7 $a10.1007/BFb0077660$2doi
035 $a(Springer)9783540477624
040 $aSpringer
050 4 $aQA613-613.8
050 4 $aQA613.6-613.66
072 7 $aPBMS$2bicssc
072 7 $aPBPH$2bicssc
072 7 $aMAT038000$2bisacsh
082 04 $a514.34$223
100 1 $aMüller, Werner,$eauthor.
245 10 $aManifolds with Cusps of Rank One :$bSpectral Theory and L2-Index Theorem /$cby Werner Müller.
264 1 $aBerlin, Heidelberg :$bSpringer Berlin Heidelberg,$c1987.
300 $aXI, 158 pp.$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 ;$v1244
505 0 $aContents: Preliminaries -- Cusps of rank one -- The heat equation on the cusp -- The Neumann Laplacian on the cusp -- Manifolds with cusps of rank one -- The spectral resolution of H -- The heat kernel -- The Eisenstein functions -- The spectral shift function -- The L -index of generalized Dirac operators -- The unipotent contribution to the index -- The Hirzebruch conjecture -- References -- Subject index -- List of notations.
520 $aThe manifolds investigated in this monograph are generalizations of (XX)-rank one locally symmetric spaces. In the first part of the book the author develops spectral theory for the differential Laplacian operator associated to the so-called generalized Dirac operators on manifolds with cusps of rank one. This includes the case of spinor Laplacians on (XX)-rank one locally symmetric spaces. The time-dependent approach to scattering theory is taken to derive the main results about the spectral resolution of these operators. The second part of the book deals with the derivation of an index formula for generalized Dirac operators on manifolds with cusps of rank one. This index formula is used to prove a conjecture of Hirzebruch concerning the relation of signature defects of cusps of Hilbert modular varieties and special values of L-series. This book is intended for readers working in the field of automorphic forms and analysis on non-compact Riemannian manifolds, and assumes a knowledge of PDE, scattering theory and harmonic analysis on semisimple Lie groups.
650 24 $aManifolds and Cell Complexes (incl. Diff.Topology)
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aCell aggregation$xMathematics.
776 08 $iPrinted edition:$z9783540176961
830 0 $aLecture Notes in Mathematics ;$v1244.
988 $a20131128
906 $0VEN