Abstract:
We consider a classical linear conjugation problem for analytic vector-valued functions on a piecewise smooth curve with a triangular matrix coefficient in weighted Hölder spaces. For the two-dimensional case, conditions for the existence of a solution are found, a solution of this problem is given, and the construction of the canonical matrix function is analyzed in detail.
Keywords:
linear conjugation problem, weighted space, canonical function.
This work was partially supported by the Ministry of Education and Science of the Russian Federation (project No. 1.7311.2017/BCh) and the Ministry of Education and Science of the Republic of Kazakhstan (international project No. 3492.GF4).
Citation:
G. N. Aver'yanov, A. P. Soldatov, “Linear conjugation problem with a triangular matrix coefficient”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 3–8; J. Math. Sci. (N. Y.), 257:1 (2021), 1–7
\Bibitem{AveSol19}
\by G.~N.~Aver'yanov, A.~P.~Soldatov
\paper Linear conjugation problem with a triangular matrix coefficient
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 3--8
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into418}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981824}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 257
\issue 1
\pages 1--7
\crossref{https://doi.org/10.1007/s10958-021-05463-7}
Linking options:
https://www.mathnet.ru/eng/into418
https://www.mathnet.ru/eng/into/v160/p3
This publication is cited in the following 2 articles:
N. K. Bliev, N. M. Yerkinbayev, “Boundary conjugation problem for piecewise analytic functions in Besov spaces”, Complex Variables and Elliptic Equations, 69:5 (2024), 849
Nazarbay Bliev, Nurlan Yerkinbayev, “Riemann problem for multiply connected domain in Besov spaces”, Bound Value Probl, 2024:1 (2024)