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Article

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Accepted version

Publication date

2019-12-15

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cc-by-nc-nd (c) Elsevier, 2019
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164420

Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions

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https://doi.org/10.1016/j.jfa.2019.108282

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.

Subject

Funcions enteres, Nuclis de Bergman, Funcions de diverses variables complexes, Anàlisi harmònica

Subject (English)

Entire functions, Bergman kernel functions, Functions of several complex variables, Harmonic analysis

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GRÖCHENIG, Karlheinz, et al. Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions. Journal of Functional Analysis. 2019. Vol. 277, num. 12. ISSN 0022-1236. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/164420

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