عنوان

Manifolds with cusps of rank one

3540477624 (electronic bk.)

9783540477624 (electronic bk.)

0387172106

0387176969

3540176969

9780387172101

9780387176963

9783540176961

b433496

Manifolds with cusps of rank one

[Book]

spectral theory and L²-index theorem /

Werner Müller

New York :

Springer-Verlag,

©1987

1 online resource (ix, 158 pages)

Lecture notes in mathematics,

1244

0075-8434 ;

"Subseries: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn, vol. 9."

Includes bibliographical references (p. [150]-154) and index

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

0

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 theory and harmonic analysis on semisimple Lie groups

Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

Manifolds with cusps of rank one.

0387172106

Index theorems

Manifolds (Mathematics)

Spectral theory (Mathematics)

Index, Théorie de l' (mathématiques)

Théorie spectrale (mathématiques)

Variétés (mathématiques)

Müller, Werner,1949-

20151023011907.0

pn

[Book]

Y