The Szegö projection need not preserve global analyticity
type: Item
instance of: scholarly article
title: The Szegö projection need not preserve global analyticity
zbMATH Open document ID: 0851.32024
DOI: 10.2307/2118645
author: Michael Christ
published in: Annals of Mathematics. Second Series
publication date: 1996-12-02T00:00:00Z
review text: Let \(\Omega\) be a pseudoconvex domain in \(\mathbb{C}^n\) with real analytic boundary \(\partial \Omega\) and \(H^2 (\partial \Omega)\) be the closed subspace of \(L^2(\partial \Omega)\), consisting of those functions that extend holomorphically to \(\Omega\). The Szegö projection \(S\) is the orthogonal projection from \(L^2(\partial \Omega)\) onto \(H^2(\partial \Omega)\) with respect to the Hilbert space structure induced by the surface measure on \(\partial \Omega\). It is known that if \(f \in C^\infty\) on \(\partial \Omega\), then also \(Sf \in C^\infty\) on \(\partial \Omega\) [\textit{J. J. Kohn}, Proc. Symp. Pure Math. 43, 207-217 (1985; Zbl 0571.58027)]. The main result of the author is: There exists a bounded pseudoconvex domain \(\Omega\) in \(\mathbb{C}^2\) with real analytic boundary and a real analytic function \(f\) on \(\partial \Omega\) such that \(Sf\) is not real analytic.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 880146
zbMATH Keywords: Szegö projection
reviewed by: Abduhamid Džuraev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118645
OpenAlex ID: W2327005295
description: scientific article; zbMATH DE number 880146