Analytic multifunctions, the \({\bar\partial}\)-equation, and a proof of the Corona theorem
type: Item
instance of: scholarly article
title: Analytic multifunctions, the \({\bar\partial}\)-equation, and a proof of the Corona theorem
zbMATH Open document ID: 0602.32002
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The purpose of this article is to give some application of a recent theorem by Alexander-Wermer and Slodkowski on the structure of certain polynomial hulls. The authors prove that this theorem gives a useful method of constructing analytic functions with prescribed properties in the disc. In particular it yields a rather easy proof of the Corona problem for two generators, and also implies Wolf's theorem on the \({\bar \partial}\)-equation.
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 30G30
Mathematics Subject Classification ID: 32E20
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 32W05
zbMATH DE Number: 3971180
zbMATH Keywords: analytic multifunction
zbMATH Keywords: polynomial hulls
zbMATH Keywords: Corona problem
zbMATH Keywords: \({\bar \partial }\)-equation
author: Bo Berndtsson
author: Thomas J. Ransford
reviewed by: S. F. Krendelev
MaRDI profile type: Publication
full work available at URL: pjm.1986.124.57
OpenAlex ID: W2166491780
DOI: 10.2140/PJM.1986.124.57
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description: scientific article; zbMATH DE number 3971180