Theory of Complex Homogeneous Bounded Domains (Mathematics and Its Applications, 569)

✍ Scribed by Yichao Xu

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 437
• Edition: 2005
• Category: Library

✦ Synopsis

This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. The Siegel domains are discussed in detail, and proofs are presented. 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.

✦ Table of Contents

Cover
Series
Title page
Date-line
Preface
Contents
Chapter 1. SIEGEL DOMAINS
1. Bounded Domains
1.1. Some Conceptions and Symbols
1.2. Bounded Domains
2. Siegel Domains
3. Holomorphic Automorphism Group of Siegel Domains
Chapter 2. HOMOGENEOUS SIEGEL DOMAINS
1. Homogeneous Bounded Domains
2. Homogeneous Siegel Domains
3. Normal $J$ Lie Algebras
4. $J$ Basis of a Normal $J$ Lie Algebra
Chapter 3. NORMAL SIEGEL DOMAINS
1. Normal Cones and Normal Siegel Domains of First Kind
2. Normal Siegel Domains
3. Decomposable Normal Siegel Domains
4. Bergman Kernel Function of Normal Siegel Domains
Chapter 4. OTHER REALIZATIONS
1. Homogeneous Bounded Domain Realization
2. $T$ Algebra Realization
Chapter 5. AUTOMORPHISM GROUP
1. Affine Automorphism Group of Normal Cones
2. Affine Automorphism Group of Normal Siegel Domains
3. Holomorphic Automorphism Group
4. Other Results
Chapter 6. CLASSIFICATION OF SQUARE DOMAINS
1. Classification of Two Special Matrix Sets
2. Normal Cones and Dual Normal Cones
3. Classification of Square Cones
4. Classification of Dual Square Cones
5. Classification of Square Domains
6. Classification of General Square Domains
Chapter 7. SYMMETRIC BOUNDED DOMAINS
1. Symmetric Bounded Domains
2. Semisimple $J$ Lie Algebras
3. Classification of Symmetric Siegel Domains
4. Realization of Exceptional Cases
Chapter 8. SZEGO KERNEL AND POISSON KERNEL
1. Cauchy-Szego Integral
2. Formal Poisson Kernel Function
3. Stein-Vagi Conjecture
4. Poisson Integral on Symmetric Siegel Domains
Chapter 9. HOMOGENEOUS BOUNDED DOMAINS
1. Non—Semisimple Effective J Lie Algebras
2. Algebraic $J$ Lie Algebras
3. Realization of Homogeneous Siegel Domains
4. Homogeneous Bounded Domains
5. Main Theorem
References
Index