Abstract:
The matrix case of a boundary value problem of linear conjugation in the theory of analytic functions, for arbitrary piecewise smooth curves, is treated, as is the corresponding adjoint problem. For these problems Noetherian theorems are proved, a family of canonical functions is constructed, and the behavior of these solutions at corner points of the curve is described.
Bibliography: 9 titles.
\Bibitem{Sol79}
\by A.~P.~Soldatov
\paper A~boundary value problem of linear conjugation in the theory of functions
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 1
\pages 175--192
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\crossref{https://doi.org/10.1070/IM1980v014n01ABEH001067}
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Linking options:
https://www.mathnet.ru/eng/im1679
https://doi.org/10.1070/IM1980v014n01ABEH001067
https://www.mathnet.ru/eng/im/v43/i1/p184
This publication is cited in the following 7 articles:
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Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 232, VINITI RAN, M., 2024, 89–98
A. B. Rasulov, Yu. S. Fedorov, “On a statement of the boundary value problem for a generalized Cauchy–Riemann equation with nonisolated singularities in a lower-order coefficient”, Math. Notes, 116:1 (2024), 119–129
N. K. Bliev, N. M. Yerkinbayev, “Boundary conjugation problem for piecewise analytic functions in Besov spaces”, Complex Variables and Elliptic Equations, 2023, 1
Yu. S. Fedorov, “A Riemann–Hilbert Type Problem for a Singularly Perturbed Cauchy–Riemann Equation with a Singularity in the Coefficient”, Diff Equat, 58:3 (2022), 367
G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem with a triangular matrix coefficient”, J. Math. Sci. (N. Y.), 257:1 (2021), 1–7
Alexander P. Soldatov, AIP Conference Proceedings, 2048, 2018, 040003
G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem for analytic functions in the weighted Hölder spaces”, Russian Math. (Iz. VUZ), 59:9 (2015), 47–50