We study the Schwarz problem for vector-valued Douglis analytic (J-analytic) functions in an ellipse, where the matrix J is diagonalizable and all its eigenvalues are located either above or below the real axis. Under the assumptions that the boundary function is Hölder on the boundary of the ellipse, we obtain necessary and sufficient conditions for the existence and uniqueness of a solution to the Schwarz problem in Hölder classes.
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Translated from Problemy Matematicheskogo Analiza101, 2019, pp. 103-116.
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Nikolaev, V.G. Solutions to the Schwarz Problem with Diagonalizable Matrices in Ellipse. J Math Sci 244, 655–670 (2020). https://doi.org/10.1007/s10958-019-04640-z
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DOI: https://doi.org/10.1007/s10958-019-04640-z