2017
Том 69
№ 6

All Issues

Integral representations of generalized axially symmetric potentials in a simply connected domain

Grishchuk S. V., Plaksa S. A.

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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.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 2, pp 195-213.

Citation Example: Grishchuk S. V., Plaksa S. A. Integral representations of generalized axially symmetric potentials in a simply connected domain // Ukr. Mat. Zh. - 2009. - 61, № 2. - pp. 160-177.

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