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2003-08

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164726

Interpolation and sampling sequences for entire functions

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https://doi.org/10.1007/s00039-003-0434-7

Abstract

We characterise interpolating and sampling sequences for the spaces of entire functions $f$ such that $f e^{-\phi}\in L^p(\C)$, $p\geq 1$ where $\phi$ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by $\Delta\phi$. They generalise previous results by Seip for the case $\phi(z)=|z|^2$, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip for the case when $\Delta\phi$ is bounded above and below, and Lyubarski\u{\i} \& Seip for 1-homogeneous weights of the form $\phi(z)=|z|h(\arg z)$, where $h$ is a trigonometrically strictly convex function.

Subject

Interpolació (Matemàtica), Funcions de variables complexes, Anàlisi funcional, Espais de Hilbert, Funcions analítiques

Subject (English)

Interpolation, Functions of complex variables, Functional analysis, Hilbert space, Analytic functions

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MARCO, Nicolás, MASSANEDA CLARES, Francesc Xavier and ORTEGA CERDÀ, Joaquim. Interpolation and sampling sequences for entire functions. Geometric and Functional Analysis. 2003. Vol. 13, num. 4, pags. 862-914. ISSN 1016-443X. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/164726

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