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Manifolds with cusps of rank one: spectral theory and L2-index theorem

The manifolds investigated in this monograph are generalizations of (Mathematical Physics and Mathematics)-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 operat...

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Detalles Bibliográficos
Autor principal: Müller, Werner
Lenguaje:eng
Publicado: Springer 1987
Materias:
Acceso en línea:https://dx.doi.org/10.1007/BFb0077660
http://cds.cern.ch/record/1691543
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author Müller, Werner
author_facet Müller, Werner
author_sort Müller, Werner
collection CERN
description The manifolds investigated in this monograph are generalizations of (Mathematical Physics and Mathematics)-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 (Mathematical Physics and Mathematics)-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.
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spelling cern-16915432021-04-21T21:09:04Zdoi:10.1007/BFb0077660http://cds.cern.ch/record/1691543engMüller, WernerManifolds with cusps of rank one: spectral theory and L2-index theoremMathematical Physics and MathematicsThe manifolds investigated in this monograph are generalizations of (Mathematical Physics and Mathematics)-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 (Mathematical Physics and Mathematics)-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.Springeroai:cds.cern.ch:16915431987
spellingShingle Mathematical Physics and Mathematics
Müller, Werner
Manifolds with cusps of rank one: spectral theory and L2-index theorem
title Manifolds with cusps of rank one: spectral theory and L2-index theorem
title_full Manifolds with cusps of rank one: spectral theory and L2-index theorem
title_fullStr Manifolds with cusps of rank one: spectral theory and L2-index theorem
title_full_unstemmed Manifolds with cusps of rank one: spectral theory and L2-index theorem
title_short Manifolds with cusps of rank one: spectral theory and L2-index theorem
title_sort manifolds with cusps of rank one: spectral theory and l2-index theorem
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BFb0077660
http://cds.cern.ch/record/1691543
work_keys_str_mv AT mullerwerner manifoldswithcuspsofrankonespectraltheoryandl2indextheorem