Beurling type density theorems in the unit disk
type: Item
instance of: scholarly article
title: Beurling type density theorems in the unit disk
zbMATH Open document ID: 0789.30025
DOI: 10.1007/BF01244300
published in: Inventiones Mathematicae
publication date: 1994-06-01T00:00:00Z
full work available at URL: https://eudml.org/doc/144120
review text: We consider two equivalent density concepts for the unit disk that provide a complete description of sampling and interpolation in \(A^{- n}\) (the Banach space of functions \(f\) analytic in the unit disk with \((1-| z |^ 2)^ n | f(z) |\) bounded). This study reveals a `Nyquist density': A sequence of points is (roughly speaking) a set of sampling if and only if its density in every part of the disk is strictly larger than \(n\), and it is a set of interpolation if and only if its density in every part of the disk is strictly smaller than \(n\). Similar density theorems are also obtained for weighted Bergman spaces.
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 549679
zbMATH Keywords: uniform densities of sequences
zbMATH Keywords: sampling
zbMATH Keywords: Bergman spaces
author: Kristian Seip
reviewed by: Kristian Seip
MaRDI profile type: Publication
cites work: Suites D'Interpolation Pour les Classes de Bergman de la Boule et du Polydisque de Cn
cites work: Interpolation in A −∞
cites work: An Interpolation Problem for Bounded Analytic Functions
cites work: Q3925395
cites work: The wavelet transform, time-frequency localization and signal analysis
cites work: A Class of Nonharmonic Fourier Series
cites work: Q5727906
cites work: An extension of the Nevanlinna theory
cites work: Necessary density conditions for sampling an interpolation of certain entire functions
cites work: Closed-ranged restriction operators on weighted Bergman spaces
cites work: Interpolation by functions in Bergman spaces
cites work: Regular Sets of Sampling and Interpolation for Weighted Bergman Spaces
cites work: Density theorems for sampling and interpolation in the Bargmann-Fock space I.
cites work: Q4006397
cites work: Q5634458
cites work: Q3955832
cites work: Q3999007
description: scientific article; zbMATH DE number 549679