Integral representation and asymptotic behavior of harmonic functions in half space |
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| Authors: | Yan Hui Zhang Kit Ian Kou Guan Tie Deng |
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| Affiliation: | 1. Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China;2. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau;3. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing, 100875, China |
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| Abstract: | Using Carleman's formula of a harmonic function in the half space and Nevanlinna's representation of a harmonic function in the half sphere, we prove that a harmonic function, whose positive part satisfies a slowly growing condition, can be represented by a certain integral. This improves some classical Poisson integrals for harmonic functions. |
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| Keywords: | Carleman's formula Nevanlinna's representation Integral representation Growth |
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