Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 277, Issue 12, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2019.108282
Keywords
Sampling and interpolation; Holomorphic functions; Reproducing kernel Hilbert spaces; Localized frames
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Funding
- WWTF grant INSIGHT [MA16-053]
- Austrian Science Fund (FWF) [P 29462-N35, P 31153-N35]
- Ministerio de Economia y Competitividad, Gobierno do Espana [MTM2017-83499-P]
- Generalitat de Catalunya [2017 SGR 358]
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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 partial derivative ) 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. (C) 2019 Elsevier Inc. All rights reserved.
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