Reduction of Vector Boundary Value Problems on Riemann Surfaces to One-Dimensional Problems
- 作者: Semenko E.1
-
隶属关系:
- Novosibirsk State Technical University Novosibirsk State Pedagogical University
- 期: 卷 60, 编号 1 (2019)
- 页面: 153-163
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172264
- DOI: https://doi.org/10.1134/S0037446619010178
- ID: 172264
如何引用文章
详细
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.
作者简介
E. Semenko
Novosibirsk State Technical University Novosibirsk State Pedagogical University
编辑信件的主要联系方式.
Email: semenko54@gmail.com
俄罗斯联邦, Novosibirsk
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