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On a Certain Functional Equation and Its Application to the Schwarz Problem

Author

Listed:
  • Vladimir Nikolaev

    (Yaroslav-the-Wise Novgorod State University, Bolshaya St.-Peterburgskaya ul. 41, 173003 Velikiy Novgorod, Russia)

  • Vladimir Vasilyev

    (Center of Applied Mathematics, Belgorod State National Research University, Pobedy St. 85, 308015 Belgorod, Russia)

Abstract

The Schwarz problem for J -analytic functions in an ellipse is considered. In this case, the matrix J is assumed to be two-dimensional with different eigenvalues located above the real axis. The Schwarz problem is reduced to an equivalent boundary value problem for the scalar functional equation depending on the real parameter l . This parameter is determined by the Jordan basis of the matrix J . An analysis of the functional equation was performed. It is shown that for l ∈ [ 0 , 1 ] , the solution of the Schwarz problem with matrix J exists uniquely in the Hölder classes in an arbitrary ellipse.

Suggested Citation

  • Vladimir Nikolaev & Vladimir Vasilyev, 2023. "On a Certain Functional Equation and Its Application to the Schwarz Problem," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2789-:d:1175652
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