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Spherical Inversion on SLn(R)

  • Jay Jorgenson
  • Serge Lang

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Jay Jorgenson, Serge Lang
    Pages 1-32
  3. Jay Jorgenson, Serge Lang
    Pages 75-129
  4. Jay Jorgenson, Serge Lang
    Pages 131-175
  5. Jay Jorgenson, Serge Lang
    Pages 177-218
  6. Jay Jorgenson, Serge Lang
    Pages 219-254
  7. Jay Jorgenson, Serge Lang
    Pages 255-275
  8. Jay Jorgenson, Serge Lang
    Pages 277-308
  9. Jay Jorgenson, Serge Lang
    Pages 309-324
  10. Jay Jorgenson, Serge Lang
    Pages 373-386
  11. Jay Jorgenson, Serge Lang
    Pages 387-410
  12. Back Matter
    Pages 411-426

About this book

Introduction

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.

Keywords

Convexity algebra differential operator integral integration lie group metric space operator proof representation theory transform theory

Authors and affiliations

  • Jay Jorgenson
    • 1
  • Serge Lang
    • 2
  1. 1.Department of MathematicsCity College of New York, CUNYNew YorkUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9302-3
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2883-2
  • Online ISBN 978-1-4684-9302-3
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site