Composition operators and generalized primes

Kouroupis, Athanasios

doi:10.1090/proc/16395

Composition operators and generalized primes
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by Athanasios Kouroupis;

Proc. Amer. Math. Soc. 151 (2023), 4291-4305

DOI: https://doi.org/10.1090/proc/16395

Published electronically: June 30, 2023

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Abstract:

We study composition operators on the Hardy space $\mathcal {H}^2$ of Dirichlet series with square summable coefficients. Our main result is a necessary condition, in terms of a Nevanlinna-type counting function, for a certain class of composition operators to be compact on $\mathcal {H}^2$. To do that we extend our notions to a Hardy space $\mathcal {H}_{\Lambda }^2$ of generalized Dirichlet series, induced in a natural way by a sequence of Beurling’s primes.

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