R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case
https://doi.org/10.26907/2541-7746.2024.2.250-261
Abstract
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.
Keywords
R-linear conjugation,
parabolic case,
factorization of matrix functions,
G.N. Chebotarev’s algorithm,
partial index
Supporting agencies: This study was supported in part by the State Program for Scientific Research of the Republic of Belarus “Convergence-2025” (project no. 1.7.01.4).
About the Authors
S. V. Rogosin
Belarusian State University
Belarus
Belarus
Minsk, 220050
L. P. Primachuk
Belarusian State University
Belarus
Belarus
Minsk, 220050
M. V. Dubatovskaya
Belarusian State University
Belarus
Belarus
Minsk, 220050
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Review
For citations:
Rogosin S.V., Primachuk L.P., Dubatovskaya M.V. R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(2):250–261. (In Russ.) https://doi.org/10.26907/2541-7746.2024.2.250-261
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