Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating...
| Authors: | ; ; ; |
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| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2019 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/164420 |
| Online Access: | https://hdl.handle.net/2445/164420 |
| Access Level: | Open access |
| Keyword: | Funcions enteres Nuclis de Bergman Funcions de diverses variables complexes Anàlisi harmònica Entire functions Bergman kernel functions Functions of several complex variables Harmonic analysis |
| Summary: | Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating. To prove optimality of the density conditions, we construct sampling sets with a density arbitrarily close to the critical density. The techniques combine methods from several complex variables (estimates for $\bar \partial$) and the theory of localized frames in general reproducing kernel Hilbert spaces (with no analyticity assumed). The abstract results on Fekete points and deformation of frames may be of independent interest. |
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