2020/12/15 by Defant, Andreas, Fernandez-Vidal, Tomas, Schoolmann, Ingo +1
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2012.08477
Inspired by a recent article on Fréchet spaces of ordinary Dirichlet series ∑ an n-s due to J.~Bonet, we study topological and geometrical properties of certain scales of Fréchet spaces of general Dirichlet spaces ∑ an e-λn s. More precisely, fixing a frequency λ= (λn), 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 [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 an e-λn/k for each k equals the Fourier coefficients of a function on an appropriate λ-Dirichlet group.