A generalization of the Poisson integral formula for the functions harmonic and biharmonic in a ball |
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Authors: | O E Yaremko |
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Institution: | 1. Penza State Pedagogical University, Penza, 440038, Russia
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Abstract: | We construct an analytic solution to the problem of extension to the unit N-dimensional ball of the potential on its values on an interior sphere. The formula generalizes the conventional Poisson formula. Bavrin’s results obtained for the two-dimensional case by methods of function theory are transferred to the N-dimensional case (N ≥ 3). We also exhibit a solution to a similar extension problem for some operator expressions depending on a potential known on an interior sphere. A connection is established between solutions to the moment problem on a segment and on a semiaxis. |
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