Zeros of functions in Hilbert spaces of Dirichlet series

DOI10.1007/s00209-012-1118-5zbMath1281.30005arXiv1206.2815OpenAlexW2074423230MaRDI QIDQ358868

Kristian Seip

Publication date: 9 August 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2815

zbMATH Keywords

Dirichlet serieszero setBlaschke conditionDirichlet-Hardy space

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Dirichlet series, exponential series and other series in one complex variable (30B50) Hardy spaces (30H10)

Related Items (10)

Dirichlet series from the infinite dimensional point of view ⋮ Approximation numbers of composition operators on \(H^p\) spaces of Dirichlet series ⋮ Some open questions in analysis for Dirichlet series ⋮ Contractive inequalities between Dirichlet and Hardy spaces ⋮ Volterra operators and Hankel forms on Bergman spaces of Dirichlet series ⋮ An inequality of Hardy-Littlewood type for Dirichlet polynomials ⋮ Some Banach spaces of Dirichlet series ⋮ Volterra operators on Hardy spaces of Dirichlet series ⋮ Composition operators and embedding theorems for some function spaces of Dirichlet series ⋮ Approximation numbers of composition operators on the \(H^2\) space of Dirichlet series

Cites Work

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• Local properties of Hilbert spaces of Dirichlet series
• A Hilbert space of Dirichlet series and systems of dilated functions in \(L^ 2(0,1)\)
• Hardy spaces of Dirichlet series and their composition operators
• The analytic continuation of interpolatory functions
• On the zeros of functions with finite Dirichlet integral and some related function spaces
• On the zeros of functions with bounded Dirichlet integrals
• On the zeros of functions in Dirichlet-type spaces
• On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
• Admissible functions for the Dirichlet space
• Local interpolation in Hilbert spaces of Dirichlet series

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