Analysis and Geometry on Complex Homogeneous Domains
Analysis and Geometry on Complex Homogeneous Domains
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DOI：
10.1007/978-1-4612-1366-6
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发表时间：
1999-12
期刊：
影响因子：
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通讯作者：
J. Faraut;S. Kaneyuki;A. Korányi;Q. Lu;Guy J. Roos;C. Birkenhake;H. Lange
中科院分区：
文献类型：
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作者：
J. Faraut;S. Kaneyuki;A. Korányi;Q. Lu;Guy J. Roos;C. Birkenhake;H. Lange
在复杂的分析和几何的一些重要的主题都涵盖在这个优秀的介绍性文本。由专家撰写的主题，每一章展开从基础到更复杂。论述是快节奏和有效的，没有妥协的证据和例子，使读者掌握的要点。最基本的域类型是有界对称域，最初由Cartan和Harish-Chandra描述和分类。两个五个部分的文字处理这些领域：一个介绍了这个问题通过理论的半单李代数（Koranyi），另一个通过约旦代数和三重系统（鲁什）。更大类的域和空间由伪厄米特对称空间和相关的R-空间提供。这些类是涵盖通过研究他们的几何和介绍和分类他们的李代数理论（Kaneyuki）。在第四部分的书，热核的对称空间属于经典李群确定（陆）。对每种情况都进行了明确的计算，给出了精确的结果，并补充了更抽象和一般的方法。还探讨了该领域的最新进展，特别是研究了复半群，其中推广了复管域和函数空间（Faraut）。这卷将是有用的作为李群理论的学生与连接到复杂的分析，或作为一个自学资源新人到外地的研究生文本。读者将在比现有文本短得多的时间内到达主题的前沿。
A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish-Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.