ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

doi:10.1016/S0252-9602(15)30037-0

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1037-1045.doi: 10.1016/S0252-9602(15)30037-0

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

刘华

Department of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China

收稿日期:2014-03-18 修回日期:2015-02-10 出版日期:2015-09-01 发布日期:2015-09-01
作者简介:Hua LIU, E-mail: hualiu@tute.edu.cn,daliuhua@163.com
基金资助:
The first author is supported by NSFC (11471250).

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

Hua LIU

Department of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China

Received:2014-03-18 Revised:2015-02-10 Online:2015-09-01 Published:2015-09-01
Supported by:
The first author is supported by NSFC (11471250).

摘要/Abstract

摘要：

In this paper analytic boundary value problems for some classical domains in Cⁿ are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function space L² on the boundary manifold. Then an easy example of several variables, the version of torus in C², is stated. For the noncommutative classical group L_I, the characteristic boundary of a kind of bounded symmetric domain in C⁴, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem on L_I, if so, the solution is given explicitly.

关键词: complex partial differential equation, analytic boundary value problem, singular integral, bounded symmetric domain

Abstract:

Key words: complex partial differential equation, analytic boundary value problem, singular integral, bounded symmetric domain

中图分类号:

32A26

刘华. ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS[J]. 数学物理学报(英文版), 2015, 35(5): 1037-1045.

Hua LIU. ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1037-1045.

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ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

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