Integral representations of generalized axially symmetric potentials in a simply connected domain |
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Authors: | S. V. Grishchuk S. A. Plaksa |
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Affiliation: | 1.Institute of Mathematics,Ukrainian National Academy of Sciences,Kiev,Ukraine |
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Abstract: | We obtain integral representations of generalized axially symmetric potentials via analytic functions of a complex variable that are defined in an arbitrary simply connected bounded domain symmetric with respect to the real axis. We prove that these integral representations establish a one-to-one correspondence between analytic functions of a complex variable that take real values on the real axis and generalized axially symmetric potentials of certain classes. |
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