Solution to a Bergman space extremal problem for non-vanishing functions
type: Item
instance of: scholarly article
title: Solution to a Bergman space extremal problem for non-vanishing functions
zbMATH Open document ID: 1257.30062
author: T. Sheil-Small
published in: Bulletin of the London Mathematical Society
publication date: 2012-08-08T00:00:00Z
Mathematics Subject Classification ID: 30H20
zbMATH DE Number: 6064199
zbMATH Keywords: harmonic product
zbMATH Keywords: extremal problems
zbMATH Keywords: minimize area problems for nonvanishing functions
MaRDI profile type: Publication
full work available at URL: bds010
OpenAlex ID: W1964091972
DOI: 10.1112/BLMS/BDS010
review text: The author gives an impressive solution to an open problem in function theory. Let \(f(z)= 1+ az+ a_2 z^2+\cdots\) with \(a\geq 0\) be analytic in \(\{|z|< 1\}\). A long standing open problem was to fiind an extremal function solution that minimizes the \(A^2\) norm, and to find, in addition, the exact value of this minimum norm. The author uses his theory of harmonic products as a basic tool. He gives a beautiful solution.
reviewed by: Dov Aharonov
description: scientific article; zbMATH DE number 6064199