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

Vladimir Nikolaev and Vladimir Vasilyev ()
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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

Mathematics, 2023, vol. 11, issue 12, 1-10

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.

Keywords: J -analytic functions; ? -holomorphic functions; matrix eigenvalue; ellipse; functional equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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