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

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Ukrainian Mathematical Journal Aims and scope

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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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    S. V. Grishchuk & S. A. Plaksa

Authors
  1. S. V. Grishchuk
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  2. S. A. Plaksa
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 2, pp. 160–177, February, 2009.

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Grishchuk, S.V., Plaksa, S.A. Integral representations of generalized axially symmetric potentials in a simply connected domain. Ukr Math J 61, 195–213 (2009). https://doi.org/10.1007/s11253-009-0209-x

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  • DOI: https://doi.org/10.1007/s11253-009-0209-x

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