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Title: | Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions |
Author: | Gröchenig, Karlheinz Haimi, Antti Ortega Cerdà, Joaquim Romero, José Luis |
Keywords: | Funcions enteres Nuclis de Bergman Funcions de diverses variables complexes Anàlisi harmònica Entire functions Bergman kernel functions Functions of several complex variables Harmonic analysis |
Issue Date: | 15-Dec-2019 |
Publisher: | Elsevier |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2019.108282 |
It is part of: | Journal of Functional Analysis, 2019, vol. 277, num. 12 |
URI: | http://hdl.handle.net/2445/164420 |
Related resource: | https://doi.org/10.1016/j.jfa.2019.108282 |
ISSN: | 0022-1236 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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