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

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Abstract

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

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Literature cited

  1. S. A. Plaksa, “Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I,” Ukr. Mat. Zh.,42, No. 11, 1509–1517 (1990).

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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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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1672–1681, December, 1990.

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Plaksa, S.A. Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. II. Ukr Math J 42, 1507–1515 (1990). https://doi.org/10.1007/BF01060822

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  • DOI: https://doi.org/10.1007/BF01060822

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