Harmonic Analysis on Compact Solvmanifolds
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602 Jonathan Brezin
Harmonic Analysis on Compact Solvmanifolds
Springer-Verlag Berlin-Heidelberg • New York 1977
Author Jonathan Paul Brezin Department of Mathematics University of North Carolina Chapel Hill, NC 27514 USA
Library of Congress Cataloging in Publication Data
Brezin, Jonathan Paul, 1943Harmonic analysis on compact solvmanifolds. (Lecture notes in mathematics ; 602) Bibliography: p. Includes index. 1. Harmonic analysis. 2. Homogeneous spaces. I. Title. II. Series. QA3.L28 no. 602 rQA~03~ 5101.8s ~5151.785j 77-221~2
AMS Subject Classifications (1970): 43A85 ISBN 3-540-08354-5 Springer-Verlag Berlin. Heidelberg. New York ISBN 0-38?-08354-5 Springer-Verlag New York • Heidelberg • Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
PREFACE
This project began at the kind s u g g e s t i o n of P r o f e s s o r R. Remmert that I consider w r i t i n g an Ergebnisse Bericht on the general theme of harmonic analysis on compact homogeneous spaces.
For a number of reasons,
treatment of the m a t e r i a l w o u l d be more appropriate. me was
I felt that a less formal Perhaps the crucial thing for
that I did not feel that there was a sufficient body of generally interesting
results in e s s e n t i a l l y final form to justify an Ergebnisse monograph.
As the
reader who follows through chapter I in detail will see, w h a t is available now is more a collection of experimental data--albeit, hard w o n - - t h a n a coherent theory. Thus the real report will have to w a i t - - p e r h a p s
five years or more.
I w o u l d like to
thank P r o f e s s o r Remmert for his encouragement, w h i c h led me to w o r k far harder to articulate my subject than I had ever thought I could. My o r i g i n a l vision was to present in as complete and elementary form as possible the work of R. Howe and of L. A u s l a n d e r and myself on inductive methods in harmonic analysis on compact h o m o g e n e o u s spaces, and compact solvmanifolds
in particular.
The b a s i c m a t e r i a l was to b e an u n p u b l i s h e d manuscript of Howe, the essence of w h i c h is §l_!, and another u n p u b l i s h e d manuscript,
this time by L. A u s l a n d e r and myself.
Our w o r k appears here as chapter II and there is some overlap with Howe's manuscript. W h e n all was said and done, original idea,
there was something vaguely dissatisfying about that
the p r o b l e m being that very little of the color and variety the field
has to off
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