[PDF] An Introduction To Bounded Symmetric Domains eBook

Author : Cho-Ho Chu
Publisher :
Page : 393 pages
File Size : 36,51 MB
Release : 2020
Category : Banach spaces
ISBN : 9789811214110

GET BOOK

Introduction. Holomorphic maps in banach spaces. Banach manifolds. Symmetric banach manifolds -- Jordan and Lie algebraic structures. Jordan algebras. Jordan triple systems. Lie algebras and Tits-Kantor-Koecher construction. Jordan and Lie structures in banach spaces. Cartan factors -- Bounded symmetric domains. Algebraic structures of symmetric manifolds. Realisation of bounded symmetric domains. Rank of a bounded symmetric domain. Boundary structures. Invariant metrics, Schwarz Lemma and dynamics. Siegel domains. Holomorphic homogeneous regular domains. Classification -- Function theory. The class S. Bloch constant and bloch maps. Banach spaces of bloch functions. Composition operators.

Author : Cho-ho Chu
Publisher : World Scientific
Page : 406 pages
File Size : 25,36 MB
Release : 2020-09-10
Category : Mathematics
ISBN : 9811214123

GET BOOK

This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment of both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching applications of this realization in complex geometry and function theory are discussed.This monograph is intended as a convenient reference for researchers and graduate students in geometric analysis, infinite dimensional holomorphy as well as functional analysis and operator theory.

Author : Leonid Lʹvovych Vaksman
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 10,86 MB
Release : 2010
Category : Mathematics
ISBN : 0821849093

GET BOOK

Explores the basic theory of quantum bounded symmetric domains. The area became active in the late 1990s at a junction of noncommutative complex analysis and extensively developing theory of quantum groups. In a surprising advance of the theory of quantum bounded symmetric domains, it turned out that many classical problems admit elegant quantum analogs. Some of those are expounded in the book.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 46,40 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475724535

GET BOOK

Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.

Author : Shoshichi Kobayashi
Publisher : World Scientific Publishing Company
Page : 161 pages
File Size : 48,49 MB
Release : 2005-11-02
Category : Mathematics
ISBN : 9813101938

GET BOOK

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.