Interpolation and Sampling Hypersurfaces for the Bargmann-Fock space in higher dimensions
We study those smooth complex hypersurfaces $W$ in $\C ^n$ having the property that all holomorphic functions of finite weighted $L^p$ norm on $W$ extend to entire functions with finite weighted $L^p$ norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem o...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2006 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/164417 |
| Acesso em linha: | https://hdl.handle.net/2445/164417 |
| Access Level: | acceso abierto |
| Palavra-chave: | Funcions meromorfes Funcions enteres Meromorphic functions Entire functions |
| Resumo: | We study those smooth complex hypersurfaces $W$ in $\C ^n$ having the property that all holomorphic functions of finite weighted $L^p$ norm on $W$ extend to entire functions with finite weighted $L^p$ norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces $W$ in $\C ^n$ such that any entire function with finite weighted $L^p$ norm is stably determined by its restriction to $W$. We provide sufficient geometric conditions on the hypersurface to be an interpolation and sampling hypersurface. The geometric conditions that imply the extension property and the restriction property are given in terms of some directional densities. |
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