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 |
| Published: |
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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| Summary: | 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 . |
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| ISSN: | 1016-1104 2345-6914 |