Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/164420
 Title: Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions Author: Gröchenig, KarlheinzHaimi, AnttiOrtega Cerdà, JoaquimRomero, José Luis Keywords: Funcions enteresNuclis de BergmanFuncions de diverses variables complexesAnàlisi harmònicaEntire functionsBergman kernel functionsFunctions of several complex variablesHarmonic 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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