Q1093047
type: Item
instance of: scholarly article
title: Fonctions intérieurs dans la boule unité de \({\mathbb C}^ n\) dont les fonctions traces sont aussi intérieurs. (Inner functions in the unit ball of \({\mathbb C}^ n\) where the trace functions are also inner functions)
zbMATH Open document ID: 0628.32008
DOI: 10.1007/BF01163290
author: Yves Dupain
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173920
review text: We solve a problem set by W. Rudin, concerning inner functions. We prove the existence of inner functions in the unit ball B of \({\mathbb{C}}^ n\), for which every slice function is inner too. Aleksandrov's original construction of an inner function involved a series which converge in the Hardy space \(H^{1/2}(B)\). We refine his method in that way that our construction involves a series of basic functions which converges in all spaces \(H^{1/2}(D)\) where D runs through the family of discs containing the origin. This requires a very precise knowledge of the localization of the sets of points defining our basic functions.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 32A30
zbMATH DE Number: 4021571
zbMATH Keywords: inner functions in the unit ball
zbMATH Keywords: inner trace functions
MaRDI profile type: Publication
cites work: Q3969178
cites work: Valeurs au bord des modules de fonctions holomorphes
cites work: A construction of inner functions on the unit ball in \(C^ p\)
cites work: Inner functions in the unit ball of \({\mathbb{C}}^ n\)
cites work: Q3958740
label: Fonctions intérieurs dans la boule unité de \({\mathbb C}^ n\) dont les fonctions traces sont aussi intérieurs. (Inner functions in the unit ball of \({\mathbb C}^ n\) where the trace functions are also inner functions)
description: scientific article; zbMATH DE number 4021571