Spherical Inversion on SLn(R) / Edition 1

Spherical Inversion on SLn(R) / Edition 1

by Jay Jorgenson, Serge Lang
     
 

ISBN-10: 0387951156

ISBN-13: 9780387951157

Pub. Date: 06/21/2001

Publisher: Springer New York

The authors have taken into account contributions by Helgason, Gangoll i, Rosenberg, and Anker from the mid-1960s to 1990. Anker's simplifica tion of spherical inversion on the Harish-Chandra Schwartz space had n ot 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

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Overview

The authors have taken into account contributions by Helgason, Gangoll i, Rosenberg, and Anker from the mid-1960s to 1990. Anker's simplifica tion of spherical inversion on the Harish-Chandra Schwartz space had n ot 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 spec ific cases of intrinsic interest. The essential features of Harish-Cha ndra theory are exhibited on SLn(R), but hundreds of pages of backgrou nd 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' cur rent research. The book will serve as a self-contained background for parts of this research.

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Product Details

ISBN-13:
9780387951157
Publisher:
Springer New York
Publication date:
06/21/2001
Series:
Springer Monographs in Mathematics Series
Edition description:
2001
Pages:
426
Product dimensions:
9.21(w) x 6.14(h) x 1.00(d)

Table of 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^1 (Even L^p) HCS Spaces
• SL_n(C)

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