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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:
It is part of: Journal of Functional Analysis, 2019, vol. 277, num. 12
Related resource:
ISSN: 0022-1236
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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