整函数插值序列的稳定性

ON THE STABILITY OF INTERPOLATING SEQUENCE FOR ENTIRE FUNCTIONS

本文证明了指数π型整函数Bπ，p，1＜p＜∞中某些实插值序列的稳定性，从而证明了存在一个和p有关的正常数δp，使得当sup|uj－j＜δp，u0＝0时，｛Gj（x）｝j∈Z为Bπ，p，1＜p＜∞的一组无条基，其中并且我们还证得是Bπ，p，1＜p＜∞的一组稳定的无条件基．

In this paper, it is proved the stability of some interpolating sequences on Bπ,p, 1 < p < ∞, which is a space of exponential type π and pointed out that there exists a positive constant δp which depends on p such that if sup |uj - j| < δp, u0 = 0, then {Gj (x)}j∈Z is an unconditional basis for Bπ,p, 1 < p < ∞, where moreover, we proved also that is a stable unconditional basis for Bπ,p.