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Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I

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Abstract

We study the Riemann boundary problem with infinite index of logarithmic order on an open rectifiable Jordan spiral-form contour, here the influence of the contour on the solvability of the problem is comparable with the influence of the argument of its coefficient. An explicit solution of the problem is constructured in the class of functions admitting weak-power singularities at the ends of a line of conjugacy.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    S. A. Plaksa

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  1. S. A. Plaksa
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1509–1517, November, 1990.

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Plaksa, S.A. Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I. Ukr Math J 42, 1351–1358 (1990). https://doi.org/10.1007/BF01066191

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  • DOI: https://doi.org/10.1007/BF01066191

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