单位圆周上正交有理函数系

Systems of Rational Functions Orthogonal on the Unit Civcle

文章考虑单位圆周上以12πdα(x)为权,极点位于单位圆外的正交有理函数的零点及核函数的收敛性。当所有极点都等于无穷远点时它们就是熟知的G.Szeg¨o[4],关于单位圆周上加权正交多项式的结果。

In this paper we consider the position of zeros of the orthogonal rational function on the unit circle with respect to the weight 1/2πdα（x） with preasigned poles, which are in the exterior of the unit disk, and the convergency of the Kernel function. If all of the poles are equal infinity, our reswhs become to the well--known. G. Szego results of the orthogonal polynomials.