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 |
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| Language: | English |
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University of Tehran
2006-12-01
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| 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 |
| id | doaj-art-9105e5d690b642cf93280876780ec0e2 |
| 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 |