A method of defining a class of linear conjugation problems for two-dimensional vector with closed-form solutions
https://doi.org/10.26907/2541-7746.2025.3.519-530
Abstract
The problem of linear conjugation for a two-dimensional piecewise analytic vector was reduced to an equivalent problem of fractional linear conjugation, and a connection between their solutions was established. It was shown that, once a particular solution of either problem is known, the canonical system of solutions of the linear conjugation problem can be written in closed form. The relations were specified between the elements of the H¨older matrix-function of the linear conjugation problem under which the fractional linear conjugation problem has a rational solution, thus enabling a closed solution of the linear conjugation problem.
About the Author
S. N. Kiyasov
Kazan Federal University
Russian Federation
Russian Federation
Sergey N. Kiyasov, Dr. Sci. (Physics and Mathematics), Associate Professor, Department of Theory of Functions and Approximations
Kazan
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Review
For citations:
Kiyasov S.N. A method of defining a class of linear conjugation problems for two-dimensional vector with closed-form solutions. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2025;167(3):519-530. (In Russ.) https://doi.org/10.26907/2541-7746.2025.3.519-530
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