二元复变函数在圆柱域上的Hilbert边值问题

On Hilbert boundary value problems for functionsof two complex variables in circular cylinder domain

讨论二元复变函数在圆柱域上的Ｈｉｌｂｅｒｔ边值问题．使用单复变函数Ｃａｕｃｈｙ型积分的Ｐｌｅｍｅｌｊ边值公式，建立二元复变函数Ｃａｕｃｈｙ型积分的Ｐｌｅｍｅｌｊ边值公式，进而给出二元复变函数在圆柱域上的Ｈｉｌｂｅｒｔ边值问题的可解性条件及其解的表示式．

ilbert boundary value problems for analytic functions of two complex variables in circular cylinder domain are discussed. Using Plemelj formula for Cauchy form integrals on functions of a complex variable, Plemelj formula for Cauchy form integrals on functions of two complex variables is given. The conditions of solvability and representative of solution for the Hilbert boundary value problems are obtained.