论文标题
一般迪里奇莱特系列的弗里奇特空间
Fréchet spaces of general Dirichlet series
论文作者
论文摘要
受到有关普通Dirichlet系列的Fréchet空间$ \ sum a_n n^{ - s} $的最新文章的启发，我们研究了dirichlet Space $ \ sum A_n E^e^e^{ - λ_ns} $fréchet空间某些尺度的拓扑和几何特性。更准确地说，修复频率$λ=（λ_n）$，我们专注于$λ$ -Dirichlet系列的fréchet空间，这些空间的限制功能限制在所有半平面上，严格比右半平面$ [\ MATHRM {RE}> 0] $。我们开发了由$λ$ -Dirichlet系列的抽象设置的抽象设置，该系列由某些可接受的规范空间$λ$ -Dirichlet系列和它们产生的融合脱颖而出，还允许定义$λ$ -Dirichlet系列的$ a_n e_n e_n e_n e e^e e^e^e^forRéchet空间适当的$λ$ -Dirichlet组的功能。
Inspired by a recent article on Fréchet spaces of ordinary Dirichlet series $\sum a_n n^{-s}$ due to J.~Bonet, we study topological and geometrical properties of certain scales of Fréchet spaces of general Dirichlet spaces $\sum a_n e^{-λ_n s}$. More precisely, fixing a frequency $λ= (λ_n)$, we focus on the Fréchet space of $λ$-Dirichlet series which have limit functions bounded on all half planes strictly smaller than the right half plane $[\mathrm{Re} >0]$. We develop an abstract setting of pre-Fréchet spaces of $λ$-Dirichlet series generated by certain admissible normed spaces of $λ$-Dirichlet series and the abscissas of convergence they generate, which allows also to define Fréchet spaces of $λ$-Dirichlet series for which $a_n e^{-λ_n/k}$ for each $k$ equals the Fourier coefficients of a function on an appropriate $λ$-Dirichlet group.
