Geodesic
Effective factorization of third order Hölder matrix function in some classes
Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 40-52
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We consider a homogeneous linear conjugation problem for a three–dimensional piecewise analytic vector on a simple smooth closed contour partitioning the plane of a complex variable into two regions. To each solution of the problem, we assign a triple of functions which are quotients of limiting values on the contour from the corresponding regions of the components of this solution. We provide identities relating the entries of $H$–continuous matrix function of the linear conjugation problem ensuring the existence of two of its solutions for which the corresponding components of the triples are proportional and the problem itself admits a solution in closed form.
Keywords: matrix function, linear conjugation problem, factorization. 
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S. N. Kiyasov. Effective factorization of third order Hölder matrix function in some classes. Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 40-52. http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a3/

[1] N.P. Vekua, Systems of singular integral equations and some boundary value problems, P. Noordhoff, Ltd., Groningen, The Netherlands, 1967 | MR | MR

[2] S.N. Kiyasov, “Contribution to the general linear conjugation problem for a piecewise analytic vector”, Sib. Math. J., 59:2 (2018), 288–294 | DOI | MR | Zbl

[3] M.C. Camara, L. Rodman, I.M. Spitkovsky, “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

[4] S.N. Kiyasov, “Some classes of linear conjugation problems for a three-dimensional vector that are solvable in closed form”, Sib. Math. J., 56:2 (2015), 313–329 | DOI | MR | Zbl

[5] S.N. Kiyasov, “Closed–form solvability of a linear conjugation problem for three-dimensional piecewise analytic vector”, Russ. Math., 64:10 (2020), 59–65 | DOI | MR | MR | Zbl | Zbl

[6] S.N. Kiyasov, “Closed form of solutions of certain linear conjugation problems for three-dimensional analytic vector”, Russ. Math., 64:2 (2020), 19–25 | DOI | MR | MR | Zbl | Zbl

[7] V.M. Adukov, “Wiener — Hopf factorization of meromorphic matrix–valued functions”, St. Petersbg. Math. J., 4:1 (1993), 51–69 | MR

[8] F.D. Gakhov, Boundary value problems, Dover Publications, Inc., New York, 1990 | MR | Zbl