Some classes of linear conjugation problems for a four-dimensional vector that are solvable in closed form
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 23-33.

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We consider the structure of the set of piecewise meromorphic solutions for a homogeneous linear conjugation problem for a four-dimensional vector. We show that in the presence of three piecewise meromorphic solutions to the linear conjugation problem it is possible to construct a canonical system of solutions to the linear conjugation problem and distinguish some classes of problems that are solvable in closed form.
Keywords: matrix-function, linear conjugation problem, factorization.
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S. N. Kiyasov. Some classes of linear conjugation problems for a four-dimensional vector that are solvable in closed form. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2019), pp. 23-33. http://geodesic.mathdoc.fr/item/IVM_2019_6_a2/

[1] Vekua N. P., Sistemy singulyarnykh integralnykh uravnenii i nekotorye granichnye zadachi, Nauka, M., 1970

[2] Litvinchuk G. S., Spitkovskii I. M., Faktorizatsiya matrits-funktsii. Ch. I, II, Dep. v VINITI 17.04.84, No 2410-84, AN USSR, Odessa, 1984

[3] Adukov V. M., “Faktorizatsiya Vinera–Khopfa kusochno-meromorfnykh matrits-funktsii”, Matem. sb., 200:8 (2011), 3–24 | DOI

[4] Gakhov F. D., “Kraevaya zadacha Rimana dlya sistemy $n$ par funktsii”, UMN, 7:4 (1952), 3–54 | MR | Zbl

[5] Camara M. C., Rodman L., Spitkovsky I. M., “One sided invertibility of matrices over commutative rings, corona problems and Toeplitz operators with matrix symbols”, Linear Algebra Appl., 459 (2014), 58–82 | DOI | MR | Zbl

[6] Kiyasov S. N., “Ob odnom dopolnenii k obschei teorii zadachi lineinogo sopryazheniya dlya kusochno analiticheskogo vektora”, Sib. matem. zhurn., 59:2 (2018), 369–377 | MR | Zbl

[7] Gakhov F. D., “Osobye sluchai kraevoi zadachi Rimana dlya sistemy $n$ par funktsii”, Izv. AN SSSR, ser. matem., 16:2 (1952), 147–156 | MR | Zbl

[8] Kiyasov S. N., “Nekotorye klassy zadach lineinogo sopryazheniya dlya trekhmernogo vektora, razreshimye v zamknutoi forme”, Sib. matem. zhurn., 56:2 (2015), 389–408 | Zbl