Geodesic
On $\mathbb{R}$-linear conjugation problem on the unit circle
Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 79-88.

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A new method of finding a solution to the $\mathbb{R}$-linear conjugation problem on the unit circle is proposed. The problem is studied under the assumption that its main coefficient is a segment of the Fourier series. The applied method is based on reducing the considered problem to the vector-matrix boundary value problem and applying the recently suggested generalization of G. N. Chebotarev's approach to the factorization of triangular matrix functions to its matrix coefficient. 
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L. Primachuk; S. Rogozin; M. Dubatovskaya. On $\mathbb{R}$-linear conjugation problem on the unit circle. Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 79-88. http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a6/

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