ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

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 fun...

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Bibliographic Details
Published in:Acta mathematica scientia Vol. 35; no. 5; pp. 1037 - 1045
Main Author: 刘华
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2015
Department of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China
Subjects:
32A26
32A40
analytic boundary value problem
bounded symmetric domain
complex partial differential equation
Schwarz问题
singular integral
开发利用
极坐标变换
经典域
解析
谐波分析
边值问题
边界值问题
32A26
32A40
complex partial differential equation
singular integral
bounded symmetric domain
analytic boundary value problem
ISSN:0252-9602, 1572-9087
Online Access:Get full text
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Summary: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 L1, 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 L1, if so, the solution is given explicitly.
Bibliography: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 L1, 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 L1, if so, the solution is given explicitly.
42-1227/O
Hua LIU （Department of Mathematics, Tianjin University of Technology and Education, Tianjin 300222, China）
complex partial differential equation; analytic boundary value problem; singular integral; bounded symmetric domain
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(15)30037-0