A Hilbert space approach to bounded analytic extension in the ball
type: Item
instance of: scholarly article
title: A Hilbert space approach to bounded analytic extension in the ball
zbMATH Open document ID: 1045.32015
author: Mihai Putinar
author: Victor Vinnikov
author: Daniel Alpay
published in: Communications on Pure and Applied Analysis
publication date: 2004-03-08T00:00:00Z
review text: We say that a \(C^1\)-map \(\varphi:\overline D\to\overline B\) of the closed unit disk into a unit ball in \(\mathbb{C}^n\) is an analytic disk transversally attached to the unit sphere if \(\varphi\) is holomorphic on \(D\), injective on \(\overline D\), \(\|\varphi(u)\|= 1\Leftrightarrow| u|= 1\) and \(\langle\varphi'(u),\varphi(u)\rangle\neq 0\) for \(| u|= 1\). The main result of the paper is the following: Theorem 2.3. Let \(A\) be an analytic disk in the unit ball of \(\mathbb{C}^n\), transversally attached to the unit sphere. Then any bounded analytic function on \(A\) admits an analytic extension to the Schur class of the ball.
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A70
Mathematics Subject Classification ID: 47A48
zbMATH DE Number: 2053223
zbMATH Keywords: Schur class
zbMATH Keywords: reproducing kernel
zbMATH Keywords: bounded analytic extension
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
full work available at URL: cpaa.2003.2.139
OpenAlex ID: W1967344415
DOI: 10.3934/CPAA.2003.2.139
description: scientific article; zbMATH DE number 2053223