有理插值算子的连续性

1.引言 设m,n为给定的非负整数,X={z_i:z_i∈C,0≤i≤s},且z_i彼此互异。所谓有理插值问题,就是对于给定的,寻求有理函数R=P/Q∈R(m,n)(即?(P)≤m,?(Q)≤n)使得 R~(j)(z_i)=y_i~(j),j=0,1,…,k_i;i=0,1,…,s。 (1.1)而与此对应的“线性化”的问题是求P/Q∈R(m,n),使得

THE CONTINUITY OF THE RATIONAL INTERPOLATING OPERATOR

Let P/Q be an (m/n) quasi-rational interpolant for the given interpolating data(F, Z). Let T_(mn) be the operator that maps (F, Z)on P/Q. It is known that the suf-ficient condition for T_(mn) to be continuous at (F, Z) in the ordinary sense is (p)=m. In this paper we prove that T_(mn) is spherically continuous at (F, Z) if and only ifP/Q has a defect zeros. A weakened conclusion about the continuty of T_(mn) is alsogiven when P/Q has positive defects.