Fonctions séparément analytiques. (Separately analytic functions)
type: Item
instance of: scholarly article
title: Fonctions séparément analytiques. (Separately analytic functions)
zbMATH Open document ID: 0682.26009
author: Jean Saint Raymond
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74875
review text: In this paper we study the functions of two real variables which are separately real-analytic. We prove that they are jointly analytic at every point except on a closed set whose projections over both axes are polar. Conversely, for any such closed set F we provide a separately analytic function whose domain of analyticity is the complement of F.
Mathematics Subject Classification ID: 26E05
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 31A05
zbMATH DE Number: 4116859
zbMATH Keywords: logarithmic capacity
zbMATH Keywords: polar sets
zbMATH Keywords: separately real-analytic
zbMATH Keywords: jointly analytic
zbMATH Keywords: separately analytic function
zbMATH Keywords: domain of analyticity
MaRDI profile type: Publication
OpenAlex ID: W2320498446
cites work: Théorie du potentiel newtonien : énergie, capacité, suites de potentiels
cites work: Analytic and plurisubharmonic functions in finite and infinite dimensional spaces. Course given at the University of Maryland, Spring 1970
cites work: Q4771241
cites work: Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^n$
DOI: 10.5802/AIF.1204
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4116859