ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

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

Abstract

Abstract:

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.

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

CLC Number:

32A26

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

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References

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