关于Gelfer函数族支撑点的性质

Properties of the support points of the class of Gelfer functions

Gelfer函数是一类在单位圆盘上满足特定条件的解析函数,它的支撑点函数具有特殊的映照性质.该函数族与一些重要函数族之间有着密切联系,通过对该函数族的研究可以了解其他函数族相关性质.借助于Schiffer边界变分和Schiffer定理,对函数族GL的支撑点进行研究,得到该函数族支撑点的几何性质.此方法对于其他函数族在相关问题的研究上开辟了新途径.

Gelfer function is one kind of analytic functions with special condition in the unitity disc. The functions of its support points have special mapping nature.The class of functions is in close connection with some important classes of functions.The related properties of some other classes of functions can be founded out through the research of the functions of support points. Schiffer interface variation and Schiffer Theorem is used to study the support points of the class of Gelfer functions. Geometric properties of the support points of the class of functions are obtained.This opens up a new way for researching related problems of some other classes of functions.