摘要
利用一个有关解析函数项级数S-可和的引理,以及对称随机级数的S-和及a.s.收敛性关系,有下列结果:一般对称随机解析函数项级数的收敛边界几乎必然是自然边界.特别地,对称随机Taylor级数,随机Dirichlet级数,随机罗朗级数等的收敛边界几乎必然是自然边界.
By use an important lemma on the S - summability of analytic series, and the S a.s. convergenec of symmetric random series. More that the boundary of convergence of general - summability and symmetric random analytic series is a natural boundary. Especially, for symmetric random Taylor series, random Diriehlet series, random Laurent series and so on, the boundaries of convergence of these series are natural boundaries.
出处
《湖北大学学报（自然科学版）》
CAS
北大核心
2006年第1期12-14,共3页
Journal of Hubei University：Natural Science
基金
国家自然科学基金(201160132)资助课题
关键词
S-可和
A.S.收敛
自然边界
对称随机级数
S - sums
almost surely convergence
natural boundary
symmetric random series
