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http://hdl.handle.net/2445/164726
Title: | Interpolation and sampling sequences for entire functions |
Author: | Marco, Nicolás Massaneda Clares, Francesc Xavier Ortega Cerdà, Joaquim |
Keywords: | Interpolació (Matemàtica) Funcions de variables complexes Anàlisi funcional Espais de Hilbert Funcions analítiques Interpolation Functions of complex variables Functional analysis Hilbert space Analytic functions |
Issue Date: | Aug-2003 |
Publisher: | Springer Verlag |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s00039-003-0434-7 |
It is part of: | Geometric and Functional Analysis, 2003, vol. 13, num. 4, p. 862-914 |
URI: | http://hdl.handle.net/2445/164726 |
Related resource: | https://doi.org/10.1007/s00039-003-0434-7 |
ISSN: | 1016-443X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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