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Interpolation and sampling sequences for entire functions
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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.
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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: 25 of June of 2026]. Available at: https://hdl.handle.net/2445/164726