Multipliers on Hilbert Spaces of Dirichlet Series
Eric Stetler

TL;DR
This paper investigates the structure of multiplier algebras on Hilbert spaces of Dirichlet series with various weighted norms, extending previous classifications and exploring new weight classes including multiplicative and number-theoretic sequences.
Contribution
It extends the classification of multipliers on Hilbert spaces of Dirichlet series to new weight classes, including multiplicative weights and number-theoretic sequences, with bounds on operator norms.
Findings
Derived bounds on operator norms of multipliers.
Classified multiplier algebras for new weight sequences.
Provided examples matching McCarthy's results under different conditions.
Abstract
In this paper, certain classes of Hilbert spaces of Dirichlet series with weighted norms and their corresponding multiplier algebras will be explored. For a sequence of positive numbers, define \[\mathcal H^\textbf{w}=\left\{\sum_{n=n_0}^\infty a_nn^{-s}:\sum_{n=n_0}^\infty |a_n|^2 w_n<\infty\right\}.\] Hedenmalm, Lindqvist and Seip considered the case in which and classified the multiplier algebra of for this space in \cite {HLS}. In \cite{M}, McCarthy classified the multipliers on when the weights are given by \[w_n=\int_0^\infty n^{-2\sigma}d\mu(\sigma),\] where is a positive Radon measure with in its support and is the smallest positive integer for which this integral is finite. Similar results will be derived assuming the weights are multiplicative, rather than given by a…
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Taxonomy
TopicsHolomorphic and Operator Theory · advanced mathematical theories · Differential Equations and Boundary Problems
