简化原理在Hilbert空间与可分Banach空间的一些应用

SOME APPLICATIONS OF PRINCIPLE OF REDUCTION IN HILBERT SPACE AND SEPARABLE BANACH SPACE

本文研究了简化原理在Hilbert空间与可分Banach空间中的一些应用,利用简化原理和独立随机元收敛准则获得了中分Banach空间随机级数的收缩原理和B-值随机Dirichlet级数简单收敛横坐标及一般随机整函数的增长性和值分布,将许多以Rademacher序列为系数的随机Tayor级数和随机Dirichlet级数的相关结果,推广到一般的具有独立对称分布系数的随机级数上去。

In this paper, we investigate some applications of principle of reduction in Hilbert space and separable Banach space. Utilizing principle of reduction and contraction principle of random series, we prove the criterion of convergence about independent random vectors in separated Banach space, and obtain the abscissa of convergence of B-valued random Dirichlet series and the growth and the distribution of valus of random entire funcition. Some corresponding results about random Tayor series and random Dirichlet series whose coefficients are Rademacher sequences are extended to random series whose coefficients are independent and symmetric distributed.