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A jump problem on a contour with limit continuum

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Abstract

We obtain a solvability condition for boundary-value problem on restoring holomorphic function by a given jump on a contour with limit continuum. An example of such contour is a graph of the function \(y = \sin \tfrac{\pi } {x}\), 0 < x ≤ 1, whose limit continuum is a segment [−i, i] of imaginary axis.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    B. A. Kats

  2. Kazan National Research Technical University, ul. K. Marksa 10, Kazan, 420111, Russia

    S. R. Mironova

  3. Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

    A. Yu. Pogodina

Authors
  1. B. A. Kats
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  2. S. R. Mironova
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  3. A. Yu. Pogodina
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Corresponding author

Correspondence to B. A. Kats.

Additional information

Original Russian Text © B.A. Kats, S.R. Mironova, and A.Yu. Pogodina, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 2, pp. 70–75.

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Kats, B.A., Mironova, S.R. & Pogodina, A.Y. A jump problem on a contour with limit continuum. Russ Math. 59, 57–61 (2015). https://doi.org/10.3103/S1066369X15020085

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  • DOI: https://doi.org/10.3103/S1066369X15020085

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