R-Linear Conjugation Problem on the Unit Circle in the Parabolic Case - S. V. Rogosin; L. P. Primachuk; M. V. Dubatovskaya (Учёные записки Казанского университета: Серия Физико-математические науки)
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.