Interpolation and sampling sequences for entire functions
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...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2003 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/164726 |
| Acesso em linha: | https://hdl.handle.net/2445/164726 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Interpolació (Matemàtica) Funcions de variables complexes Anàlisi funcional Espais de Hilbert Funcions analítiques Interpolation Functions of complex variables Functional analysis Hilbert space Analytic functions |
| Resumo: | 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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