Geodesic
$\mathbb R$-linear conjugation problem on the unit circle in the parabolic case
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 2, pp. 250-261

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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.
Keywords: $\mathbb R$-linear conjugation, parabolic case, factorization of matrix functions, partial index.
Mots-clés : G.N. Chebotarev’s algorithm 
@article{UZKU_2024_166_2_a8,
     author = {S. V. Rogozin and L. P. Primachuk and M. V. Dubatovskaya},
     title = {$\mathbb R$-linear conjugation problem on the unit circle in the parabolic case},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {250--261},
     publisher = {mathdoc},
     volume = {166},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2024_166_2_a8/}
}
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S. V. Rogozin; L. P. Primachuk; M. V. Dubatovskaya. $\mathbb R$-linear conjugation problem on the unit circle in the parabolic case. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 2, pp. 250-261. http://geodesic.mathdoc.fr/item/UZKU_2024_166_2_a8/