多圆柱区域边界上的多复变函数是区域内多元解析函数边界值的充要条件

NECESSARY AND SUFFICIENT CONDITON OF A COMPLEXVALUED FUNCTION IN THE BOUNDARY OF A POLYDISC AS THE BOUNDARY VALUE OF SOME ANALYTIC FUNCTION OF SEVERAL COMPLEX VARIABLES IN THE POLYDISC

本文证明了复C^n空间中的多圆柱区域D=D_i边界S上定义的一个复值函数φ(z)是D内的某个n元解析函数的边界值的充要条件.作为这个条件的一个直接应用,获得了C^2空间中双圆柱区域的特征边界上的复值函数定义的柯西型积分是柯西积分的充要条件.

This paper discusses the following problem:under what conditions a complex-valued function φ(z) defined on S , the boundary surface of a polydise D =,are the boundary value of some analytic functn of several complex variables in D , then obtains the necessary and sufficient condition; φ(z) is analytic with respect Z_a(a≠k) on S_k(S_k= D_k×D_i) . By applying the condition gets the necessary and sufficient condition that a Cauchy tape integral in the bicylinder of the complex space C^2 is a Cauchy integral.