Abstract
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 \(\sum a_n e^{-\lambda _n s}\) focus on the Fréchet space of \(\lambda \)-Dirichlet series \(\sum a_n e^{-\lambda _n s}\) 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 \(\lambda \)-Dirichlet series generated by certain admissible normed spaces of \(\lambda \)-Dirichlet series and the abscissas of convergence they generate, which allows also to define Fréchet spaces of \(\lambda \)-Dirichlet series for which \(a_n e^{-\lambda _n/k}\) for each k equals the Fourier coefficients of a function on an appropriate \(\lambda \)-Dirichlet group.
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Andreas Defant: Partially supported by MINECO and FEDER project MTM2017-83262-C2-1-P.
Tomás Fernández Vidal: Supported by PICT 2015-2299.
Pablo Sevilla-Peris:Supported by MINECO and FEDER project MTM2017-83262-C2-1-P.
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Defant, A., Fernández Vidal, T., Schoolmann, I. et al. Fréchet spaces of general Dirichlet series. RACSAM 115, 138 (2021). https://doi.org/10.1007/s13398-021-01074-8
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DOI: https://doi.org/10.1007/s13398-021-01074-8