The Research Of A Kind Of Boundary Value Problem For Holomorphic Funtion

The boundary value problems for holomorphic function are so important branches in the functions of a complex variable. Because many practical problems could been changed to the boundary value problems for holomorphic function or singular integral equations in the mechanics, physics and the engineering technology. And singular integral equations have tight relation of the boundary value problems for holomorphic function. Therefore, researching these problems have important practical meaning and attracting many scientific researchers to study. It is that the Riemann boundary value problems for holomorphic function are the important aspects to research. And by study they obtained a lot of results. But we can generalize and study the Riemann boundary value problems for holomorphic function more.Then they will become more perfection and enrichment. Base on the former reserach, I mainly discuss the Riemann boundary value problems for analytic function as follows:for all positive integer m, n, and G(t) ≠ 0 at L, then L is a smooth closed curve or an infinite straight line in coplex plane and is made up of multiply smooth closed curves in coplex plane.The main content and achievement of this paper are as follows:1 , when L is a smooth closed curve in complex plane,the solutions of the above Riemann boundary value problems are respectively discussed as follows:(1) G(t) is a continuous H fuction at L;(2) G(t) is a continuous H fuction except finite the first discontinuous points at L.2 , The solutions of the above Riemann boundary value problems are discussed when the L is made up of multiply simple smooth closed curves.3 , The solutions of the above Riemann boundary value problems are discussed when the L is an infinite straight line...