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Lie Group Actions in Complex Analysis

Asped~f

Mathematic~

Edited by Klas Diederich Vol. E 2:

M. Knebusch/M. Kolster: Wiltrings

Vol. E 3:

G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part B

Vol. E 5:

P. Stiller: Automorphic Forms and the Picard Number of an Elliptic Surface

Vol. E 6:

G. Faltings/G. Wustholz et al.: Rational Points*

Vol. E 7:

W. Stoll: Value Distribution Theory for Meromorphic Maps

Vol. E 9:

A. Howard/P.-M. Wong (Eds.): Contribution to Several Complex Variables

Vol. E 10: A. J Tromba (Ed.): Seminar of New Results in Nonlinear Partial Differential Equations* Vol. E 13: Y. Andre: G-Functions and Geometry* Vol. E 14: U. Cegrell: Capacities in Complex Analysis Vol. E 15: J-P. Serre: Lectures on the Mordell-Weil Theorem Vol. E 16: K. Iwasaki/H. Kimura/S. Shimomura/M. Yoshida: From Gauss to PainlevE Vol. E 17:

K. Diederich (Ed.): Complex Analysis

Vol. E 18: W. W. J Hulsbergen: Conjectures in Arithmetic Algebraic Geometry Vol. E 19:

R. Racke: Lectures on Nonlinear Evolution Equations

Vol. E 20:

F. Hirzebruch, Th. Berger, R. Jung: Manifolds and Modular Forms*

Vol. E 21:

H. FUjimoto: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

Vol. E 22:

D.

V. Anosov/ A. A. Bolibruch: The Riemann-Hilbert Problem

Vol. E 23: A. P. Fordy/J. C. Wood (Eds.): Harmonic Maps and Integrable Systems Vol. E 24:

D. S. Alexander: A History of Complex DynamiCS

Vol. E 25:

A. Tikhomirov/A. Tyurin (Eds.): Algebraic Geometry and its Applications

Vol. E 26:

H. Skoda/J-M. Trepreau (Eds.): Contributions to Complex Analysis and Analytic Geometry

Vol. E 27:

D. N. Akhiezer: lie Group Actions in Complex Analysis

* A Publication of the Max-Planck-Institut fur Mathematik, Bonn Volumes of the German-language subseries "Aspekte der Mathematik" are listed at the end of the book.

Dmitri N. Akhiezer

Lie Group Actions in COlllple.x Analysis

Dmitri N. Akhiezer 129010 Moskau B. Spasskaja 33, KV 33 Russia

CIP-Codierung angefordert

All rights reserved © Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweiglWiesbaden, 1995 Softcoverreprintof the hardcover 1st edition 1995 Vieweg is a subsidiary company of the Bertelsmann Professional Information.

No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder.

Cover design: Wolfgang Nieger, Wiesbaden Printed on acid-free paper ISSN 0179-2156 e-ISBN-13 :978-3-322-80267-5 ISBN-13 :978-3-322-80269-9 DOl: 10.1007/978-3-322-80267-5

v

Preface

This book was planned as an introduction to a vast area, where many contributions have been made in recent years. The choice of material is based on my understanding of the role of Lie groups in complex analysis. On the one hand, they appear as the automorphism groups of certain complex spaces, e.g., bounded domains in or compact spaces, and are therefore important as being one of their invariants. On the other hand, complex Lie groups and, more generally, homogeneous co

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