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arXiv · 1505.02944

Compact composition operators with non-linear symbols on the $H^2$ space of Dirichlet series

Frédéric Bayart·Ole Fredrik Brevig
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Abstract

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $φ(s)=c_0s+φ_0(s)$, where $φ_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic $c_0$ of $φ$ and, when $c_0=0$, on both the degree of $φ_0$ and its local behaviour near a boundary point. We also study the approximation numbers for some of these operators. Our methods involve geometric estimates of Carleson measures and tools from differential geometry.

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Frédéric Bayart, Ole Fredrik Brevig. 2015-05-12. Compact composition operators with non-linear symbols on the $H^2$ space of Dirichlet series. https://doi.org/10.2140/pjm.2017.291.81

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