R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case

R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case

A solution to the R-linear conjugation problem (Markushevich boundary value problem) on the unit circle was proposed. This problem is analogous to the vector-matrix Riemann boundary value problem with the coefficient degenerating in the parabolic case (the coefficient is a triangular matrix function). A...

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Bibliographic Details
Main Authors: S. V. Rogosin, L. P. Primachuk, M. V. Dubatovskaya
Format: Article
Language:English
Published: Kazan Federal University 2024-07-01
Series:Учёные записки Казанского университета: Серия Физико-математические науки
Subjects:
r-linear conjugation
parabolic case
factorization of matrix functions
g.n. chebotarev’s algorithm
partial index
Online Access:https://uzakufismat.elpub.ru/jour/article/view/73
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Summary:A solution to the R-linear conjugation problem (Markushevich boundary value problem) on the unit circle was proposed. This problem is analogous to the vector-matrix Riemann boundary value problem with the coefficient degenerating in the parabolic case (the coefficient is a triangular matrix function). A complete description of the factorization of the matrix coefficient was provided. Its partial indices were calculated. The method used is based on G.N. Chebotarev’s algorithm and has been developed in a series of author’s articles. The resulting factorization confirms the solvability of the R-linear conjugation problem on the unit circle in the parabolic case.
ISSN:2541-7746
2500-2198

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