Analysis and Geometry on Complex Homogeneous Domains: (185 Progress in Mathematics)

[see attached] This excellent introductory text covers a number of important areas in complex analysis and geometry. Written by experts in their respective fields, each of the five chapters unfolds from the basics to the more complex. Unlike other more laborious introductory texts, the exposition here is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. Topics covered include: function spaces on complex semigroups * graded Lie algebras, related geometric structures, and pseudo- Hermitian symmetric spaces * function spaces on bounded symmetric

Table of Contents:
I Function Spaces on Complex Semi-groups by Jacques Faraut.- I Hilbert Spaces of Holomorphic Functions.- II Invariant Cones and Complex Semi-groups.- III Positive Unitary Representations.- IV Hilbert Function Spaces on Complex Semi-groups.- V Hilbert Function Spaces on SL(2,?).- VI Hilbert Function Spaces on a Complex Semi-simple Lie Group.- II Graded Lie Algebras and Pseudo-hermitian Symmetric Spaces by Soji Kaneyuki.- I Semisimple Graded Lie Algebras.- II Symmetric R-Spaces.- III Pseudo-Hermitian Symmetric Spaces.- III Function Spaces on Bounded Symmetric Domains by Adam Kordnyi.- I Bergman Kernel and Bergman Metric.- II Symmetric Domains and Symmetric Spaces.- III Construction of the Hermitian Symmetric Spaces.- IV Structure of Symmetric Domains.- V The Weighted Bergman Spaces.- VI Differential Operators.- VII Function Spaces.- IV The Heat Kernels of Non Compact Symmetric Spaces by Qi-keng Lu.- I Introduction.- II The Laplace-Beltrami Operator in Various Coordinates.- III The Integral Transformations.- IV The Heat Kernel of the Hyperball R?(m, n).- V The Harmonic Forms on the Complex Grassmann Manifold.- VI The Horo-hypercircle Coordinate of a Complex Hyperball.- VII The Heat Kernel of RII(m).- VIII The Matrix Representation of NIRGSS.- V Jordan Triple Systems by Guy Roos.- I Polynomial Identities.- II Jordan Algebras.- III The Quasi-inverse.- IV The Generic Minimal Polynomial.- V Tripotents and Peirce Decomposition.- VI Hermitian Positive JTS.- VII Further Results and Open Problems.

Review :
"The book is clearly an important contribution to the literature on the subject. A number of results presented here is not accessible in book form elsewhere. Both research students and professional mathematicians will find this valuable volume an extremely useful guide and reference work." --Publicationes Mathematicae "This book, which is a useful text for advanced graduate students and researchers...gives a comprehensive account of the field of homogeneous complex domains...The exposition is rapidly paced and efficient, without compromising proofs. Moreover, plenty of examples are given, enabling the reader to understand the essential ideas behind the notions and the theorems." --ZAA "This book has been written by five outstanding experts with the intention of surveying the most important goals and viewpoints of the field...It is a pleasant reading, details of proofs are supplied or omitted in a very well chosen manner...Many new top results are described and it contains the most important references after each part. I recommend it first of all since, using this book, one can reach the research level with considerably less effort than by the aid of other means of the recent literature." --ASM