整Dirichlet级数表示的函数空间  

Function spaces of entire Dirichlet series

作　　者：宁菊红[1] 项梦娟 NING Juhong;XIANG Mengjuan(College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, Chin)

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《黑龙江大学自然科学学报》2018年第2期171-174,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11661044)

摘　　要：给出整Dirichlet级数线性空间F的定义,利用Dirichlet级数和泛函分析相关理论,在‖·‖1范数下,证明F是一个含幺元的可交换不可除Banach代数,得到F中的元素可逆或是拓扑零因子的充要条件;在‖·‖2范数下,得到F上线性泛函连续的充要条件。The definition of the linear space F of entire Dirichlet series is given . By using the theories of Diriehlet series and functional analysis, under Ⅱ·Ⅱ1 norm it is proven that F is a commutative and not a division Banach algebra with identity, and necessary and sufficient conditions for the element invertible and topological zero divisor are given; under Ⅱ·Ⅱ2 norm, a necessary and sufficient condition for the continuous linear functional on the space F is given.

关 键 词：DIRICHLET级数 BANACH代数 拓扑零因子 可除代数 连续线性泛函 

分 类 号：O174.5[理学—数学]