**CBMS Regional Conference Series in Mathematics**

Volume: 61;
1986;
77 pp;
Softcover

MSC: Primary 43;
Secondary 22

Print ISBN: 978-0-8218-0711-8

Product Code: CBMS/61

List Price: $25.00

Individual Price: $20.00

**Electronic ISBN: 978-1-4704-2422-0
Product Code: CBMS/61.E**

List Price: $25.00

Individual Price: $20.00

# Analysis on Non-Riemannian Symmetric Spaces

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*Mogens Flensted-Jensen*

A co-publication of the AMS and CBMS

Harmonic analysis on Riemannian semisimple symmetric spaces and on
special types of non-Riemannian semisimple symmetric spaces are
well-established theories. This book presents a
systematic treatment of the basic problems on semisimple symmetric
spaces and a discussion of some of the more important recent
developments in the field. The author's primary contribution has been
his idea of how to construct the discrete series for such a space. In
this book a fundamental role is played by the ideas behind that
construction, namely the duality principle, the orbit picture related
to it, and the definition of representations by means of distributions
on the orbits.

Intended as a text at the upper graduate level, the book assumes a
basic knowledge of Fourier analysis, differential geometry,
and functional analysis. In particular, the reader should have a good
knowledge of the general theory of real and complex Lie algebras and
Lie groups and of the root and weight theories for semisimple Lie
algebras and Lie groups.

#### Table of Contents

# Table of Contents

## Analysis on Non-Riemannian Symmetric Spaces

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Acknowledgments vii8 free
- Introduction ix10 free
- I. Structure and Classification of Symmetrie Spaces 112 free
- II. Harmonic Analysis on Semisimple Symmetric Spaces 1324
- III. The Noncompact Riemannian Form X[sup(r)] of a Semisimple Symmetrie Space X 2536
- IV. The Poisson Transform on a Symmetric Space of the Noncompact Type 3344
- V. The H[sup(d)]-Orbits on the Boundary of X[sup(r)] and the Corresponding Representations of G 4354
- VI. Representations Related to the Closed H[sup(d)]-Orbits 4960
- VII. The Discrete Series for a Semisimple Symmetric Space 6172
- VIII. Few Final Remarks 6980
- Bibliography 7384
- Back Cover Back Cover189