Theory Of Complex Homogeneous Bounded Domains

This book studies the classification and function theory of complex homogenous bounded domains systematically for the first time. In it, the Siegel domains are discussed in detail. Proofs are given for

Every homogeneous bounded domains is holomorphically isomorphic to a homogeneous Siegel domain, and every homogeneous Siegel domain is affine isomorphic to a normal Siegel domain.

Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.

This book is suitable for graduate students, and researchers in mathematics.

Contents

Preface
Chapter 1. SIEGEL DOMAINS
Chapter 2. HOMGENEOUS SIEGEL DOMAINS
Chapter 3. NORMAL SIEGEL DOMAINS
Chapter 4. OTHER REALIZATIONS
Chapter 5. AUTOMORPHISM GROUP
Chapter 6. CLASSIFICATION OF SQUARE DOMAINS
Chapter 7. SYMMETRIC BOUNDED DOMAINS
Chapter 8. SZEGO KERNEL AND POISSON KERNEL
Chapter 9. HOMOGENEOUS BOUNDED DOMAINS
References
Index