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abscissas of convergence

Proceedings of the Edinburgh Mathematical Society (1)

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The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series
Part of
José Bonet
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 4 / November 2018

Published online by Cambridge University Press:

07 May 2018, pp. 933-942
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The algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not a Q-algebra. Composition operators on this space are also studied.