关于上密度无限的随机指数多项式的完备性

Completeness of the Random Exponential Polynomial with Unrestricted upper Density Gaps

本文讨论的对象为含重点的复随机指数系E(A(ω)),得到在加权Banach空间Lα^p中依概率1不完备的一个充要条件,其中Lα^p(1≤p<∞)是由实直线ER上的复可测函数组成的函数空间.

In this paper, we mainly study the complex random exponential system. A sufficient condition is obtained for the minimality of the complex random exponential system E(A(ω))={tk eλn(ω)t:k = 0.1, 2,…,μn(ω)-1; n=1, 2, 3,…} in the Banach space.