1. Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
- Author
-
Antti Haimi, José Luis Romero, Joaquim Ortega-Cerdà, and Karlheinz Gröchenig
- Subjects
Pure mathematics ,Entire function ,Functions of several complex variables ,Holomorphic function ,Nuclis de Bergman ,01 natural sciences ,Fock space ,Harmonic analysis ,symbols.namesake ,0103 physical sciences ,Several complex variables ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Complex Variables (math.CV) ,0101 mathematics ,Mathematics ,Mathematics - Complex Variables ,010102 general mathematics ,Hilbert space ,Sampling (statistics) ,Anàlisi harmònica ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Bergman kernel functions ,Funcions enteres ,Mathematics - Classical Analysis and ODEs ,Kernel (statistics) ,32A15, 32A36, 32A50, 32A60, 42C15 ,symbols ,Funcions de diverses variables complexes ,010307 mathematical physics ,Entire functions ,Analysis ,Interpolation - 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., 33 pages
- Published
- 2019