$\mathbb R$-linear conjugation problem on the unit circle in the parabolic case

S. V. Rogozin   ; L. P. Primachuk   ; M. V. Dubatovskaya

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 2, pp. 250-261

Résumé

A solution to the $\mathbb R$-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 $\mathbb R$-linear conjugation problem on the unit circle in the parabolic case.

Détail

Keywords: $\mathbb R$-linear conjugation, parabolic case, factorization of matrix functions, partial index.
Mots-clés : G.N. Chebotarev’s algorithm

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