半平面中解析函数的积分表示及在逼近中的应用

Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation

在该文中,作者证明了满足一定增长性条件的右半平面上的解析函数可以由它在边界上的积分和其加权Blaschke乘积的和表示,作为应用,作者还考虑了指数多项式在实数轴上加权Banach空间C_α中的完备性.

In this paper, we prove that analytic functions in the right halt plane with some restricted growth can be represented by a sum of its weighted Blaschke product and its integral on the boundary of the half plane. As its applications, we also investigate the completeness of complex exponential polynomials in Cα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f（t）exp（-α（t）） vanishing at infinity, in the uniform norm with respect to the weight α（t）.