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© 2001

Spherical Inversion on SLn(R)

Book

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

  1. 1.Department of MathematicsCity College of New York, CUNYNew YorkUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title Spherical Inversion on SLn(R)
  • Authors Jay Jorgenson
    Serge Lang
  • Series Title Springer Monographs in Mathematics
  • 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
  • Hardcover ISBN 978-0-387-95115-7
  • Softcover ISBN 978-1-4419-2883-2
  • eBook ISBN 978-1-4684-9302-3
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XX, 426
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Topological Groups, Lie Groups
  • Buy this book on publisher's site

Reviews

From the reviews:

"[This] book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts of Lie groups and representation theory and outsiders who would like to see connections of some aspects with other parts of mathematics. This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured." -Sergio Console, Zentralblatt

"This book is devoted to Harish-Chandra’s Plancherel inversion formula in the special case of the group SLn(R) and for spherical functions. ... the book is easily accessible and essentially self contained." (A. Cap, Monatshefte für Mathematik, Vol. 140 (2), 2003)

"Roughly, this book offers a ‘functorial exposition’ of the theory of spherical functions developed in the late 1950s by Harish-Chandra, who never used the word ‘functor’. More seriously, the authors make a considerable effort to communicate the theory to ‘an outsider’. .... However, even an expert will notice several new and pleasing results like the smooth version of the Chevally restriction theorem in Chapter 1." (Tomasz Przebinda, Mathematical Reviews, Issue 2002 j)

"This excellent book is an original presentation of Harish-Chandra’s general results ... . Unlike previous expositions which dealt with general Lie groups, the present book presents the essential features of the theory on SLn(R). This makes the book accessible to a wide class of readers, including nonexperts ... . This feature is widely to be appreciated, together with the clearness of exposition and the way the book is structured. Very nice is, for instance, the ... table of the decompositions of Lie groups." (Sergio Console, Zentralblatt MATH, Vol. 973, 2001)