论文标题
矢量值得一般的迪里奇莱特系列
Vector-valued general Dirichlet series
论文作者
论文摘要
由于H. Bohr，Hardy-Riesz，Bohnenblust-Hille，Neder和Landau的早期贡献，过去20年的开放表明，对于普通的Dirichlet系列$ \ sum a_n n n^{-s s} $的系统研究的复兴，甚至在最近的Dirichlet $ \ sum $ \ sum sum sum a__n e_n e__n e_n e___________________-这涉及将古典工作与现代功能分析，谐波分析，无限尺寸霍明型和概率理论以及分析数理论相互交织。通过这一研究的动机，本文的主要目标是对矢量值为dirichlet系列$ \ sum a_n e^{ - λ_{n} s} $的各种基本方面进行系统研究，因此，dirichlet系列，因此，在$ \ mathbb {c c} $ in in Mathbb in in in Mathbb in coff中不一定是coffice coffsic的$ \ {c {
Opened up by early contributions due to, among others, H. Bohr, Hardy-Riesz, Bohnenblust-Hille, Neder and Landau the last 20 years show a substantial revival of systematic research on ordinary Dirichlet series $\sum a_n n^{-s}$, and more recently even on general Dirichlet series $\sum a_n e^{-λ_n s}$. This involves the intertwining of classical work with modern functional analysis, harmonic analysis, infinite dimensional holomorphy and probability theory as well as analytic number theory. Motivated through this line of research the main goal of this article is to start a systematic study of a variety of fundamental aspects of vector-valued general Dirichlet series $\sum a_n e^{-λ_{n} s}$, so Dirichlet series, where the coefficient are not necessarily in $\mathbb{C}$ but in some arbitrary Banach space $X$.
