On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given functi...

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Format: Article
Language:English
Published: University of Tehran 2006-12-01
Series:Journal of Sciences, Islamic Republic of Iran
Online Access:https://jsciences.ut.ac.ir/article_31776_20b1410860bbdfdbb9970b94fea36956.pdf
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collection DOAJ
description Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations for and . The main result of this paper indicates that the dilations are convergent to in the mean, or in the norm of .
format Article
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institution OA Journals
issn 1016-1104
2345-6914
language English
publishDate 2006-12-01
publisher University of Tehran
record_format Article
series Journal of Sciences, Islamic Republic of Iran
spelling doaj-art-9105e5d690b642cf93280876780ec0e22025-08-20T02:25:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142006-12-0117431776On The Mean Convergence of Biharmonic FunctionsLet denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations for and . The main result of this paper indicates that the dilations are convergent to in the mean, or in the norm of .https://jsciences.ut.ac.ir/article_31776_20b1410860bbdfdbb9970b94fea36956.pdf
spellingShingle On The Mean Convergence of Biharmonic Functions
Journal of Sciences, Islamic Republic of Iran
title On The Mean Convergence of Biharmonic Functions
title_full On The Mean Convergence of Biharmonic Functions
title_fullStr On The Mean Convergence of Biharmonic Functions
title_full_unstemmed On The Mean Convergence of Biharmonic Functions
title_short On The Mean Convergence of Biharmonic Functions
title_sort on the mean convergence of biharmonic functions
url https://jsciences.ut.ac.ir/article_31776_20b1410860bbdfdbb9970b94fea36956.pdf