Manifolds with Cusps of Rank One : Spectral Theory and L2-Index Theorem. 1st ed. 1987

種類:

電子ブック

責任表示:

by Werner Müller

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1987

著者名:

• Müller, Werner.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1244

ISBN:

9783540477624 [3540477624]    

注記:

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 L2-index of generalized dirac operators -- The unipotent contribution to the index -- The Hirzebruch conjecture.
The 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 theor

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