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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
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:
It is part of: Geometric and Functional Analysis, 2003, vol. 13, num. 4, p. 862-914
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ISSN: 1016-443X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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