Norm approximation by polynomials in some weighted Bergman spaces
type: Item
instance of: scholarly article
title: Norm approximation by polynomials in some weighted Bergman spaces
zbMATH Open document ID: 1059.30049
author: A. Abkar
published in: Journal of Functional Analysis
publication date: 2002-09-08T00:00:00Z
review text: In this paper the author shows that the polynomials are dense in weighted Bergman spaces in the unit disc whose weights are superbiharmonic functions and vanish in an average sense at the boundary. This result yields an alternative proof of the Aleman Richter-Sundberg Beurling-type theorem related to the zero-based invariant subspaces in the classical Bergman space. Further, the author obtains several consequences.
reviewed by: G. Kohr
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 46E22
zbMATH DE Number: 1797588
zbMATH Keywords: Bergman space, Hardy space
zbMATH Keywords: harmonic compensator
zbMATH Keywords: superbiharmonic function
zbMATH Keywords: weight function
zbMATH Keywords: biharmonic Green function
MaRDI profile type: Publication
full work available at URL: jfan.2001.3851
OpenAlex ID: W1999016178
cites work: Q4799683
cites work: Beurling's theorem for the Bergman space
cites work: Q5618011
cites work: Linear and complex analysis problem book 3. Part 2
cites work: A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
cites work: A Factoring Theorem for The Bergman Space
cites work: Q4490700
cites work: On the completeness of systems of analytic functions
DOI: 10.1006/JFAN.2001.3851
description: scientific article; zbMATH DE number 1797588