Résumé
Harish-Chandra's general Plancherel inversion theorem
admits a much shorter presentation for spherical functions.
The authors have taken into account contributions by
Helgason, Gangolli, Rosenberg, and Anker from the mid-1960s
to 1990. Anker's simplification of spherical inversion on
the Harish-Chandra Schwartz space had not yet made it into
a book exposition. Previous expositions have dealt with a
general, wide class of Lie groups. This has made access to
the subject difficult for outsiders, who may wish to
connect some aspects with several if not all other parts of
mathematics, and do so in specific cases of intrinsic
interest. The essential features of Harish-Chandra theory
are exhibited on SLn(R), but hundreds of pages of
background can be replaced by short direct verifications.
The material becomes accessible to graduate students with
especially no background in Lie groups and representation
theory. Spherical inversion is sufficient to deal with the
heat kernel, which is at the center of the authors' current
research. The book will serve as a self-contained
background for parts of this research.
Contents
- Iwasawa Decomposition and Positivity
- Invariant Differential Operators and the Iwasawa Direct Image
- Characters, Eigenfunctions, Spherical Kernel and W-Invariance
- Convolutions, Spherical Functions and the Mellin Transform
- Gelfand-Naimark Decomposition and the Harish-Chandra -Function
- Polar Decomposition
- The Casimir Operator
- The Harish-Chandra Series for Eigenfunctions of Casimir
- General Inversion
- The Harish-Chandra Schwartz Space (HCS) and Anker's Proof of Inversion
- Tube Domains and the L (Even Lp) HCS Spaces
- SLn(C)
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Jay Jorgenson, Serge A. Lang |
| Parution | 15/07/2001 |
| Nb. de pages | 426 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 790g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780387951157 |
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