Reduction of Vector Boundary Value Problems on Riemann Surfaces to One-Dimensional Problems
- Авторы: Semenko E.1
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Учреждения:
- Novosibirsk State Technical University Novosibirsk State Pedagogical University
- Выпуск: Том 60, № 1 (2019)
- Страницы: 153-163
- Раздел: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172264
- DOI: https://doi.org/10.1134/S0037446619010178
- ID: 172264
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Аннотация
This article lays foundations for the theory of vector conjugation boundary value problems on a compact Riemann surface of arbitrary positive genus. The main constructions of the classical theory of vector boundary value problems on the plane are carried over to Riemann surfaces: reduction of the problem to a system of integral equations on a contour, the concepts of companion and adjoint problems, as well as their connection with the original problem, the construction of a meromorphic matrix solution. We show that each vector conjugation boundary value problem reduces to a problem with a triangular coefficient matrix, which in fact reduces the problem to a succession of one-dimensional problems. This reduction to the well-understood one-dimensional problems opens up a path towards a complete construction of the general solution of vector boundary value problems on Riemann surfaces.
Об авторах
E. Semenko
Novosibirsk State Technical University Novosibirsk State Pedagogical University
Автор, ответственный за переписку.
Email: semenko54@gmail.com
Россия, Novosibirsk
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