加权Banach空间中指数函数系完备的稳定性

摘要

本文研究了加权Banach空间中指数函数系完备的稳定性问题.利用解析函数扰动的方法,获得了加权Banach空间中指数函数系完备的稳定性若干结果,推广了现有有限区间Banach空间上的经典结果.%In this paper, we study the stability of completeness of exponential systems in weighted Banach spaces. Using the method of perturbation of analytic functions, we obtain several new results on stability. Our results can be regarded as generalization of some existing classical theorems which consider the same problem on Banach spaces over finite intervals.