Contribution to the general linear conjugation problem for a piecewise analytic vector. (English. Russian original) Zbl 1402.30038
Sib. Math. J. 59, No. 2, 288-294 (2018); translation from Sib. Mat. Zh. 59, No. 2, 369-377 (2018).
An algorithm is discussed for constructing a canonical system of solutions to the homogeneous linear conjugation problem for \(n\) pairs of functions, provided that \(n-1\) linearly independent solutions are given.
Reviewer: Ilya Spitkovsky (Williamsburg)
MSC:
| 30E25 | Boundary value problems in the complex plane |
References:
| [1] | Vekua N. P., Systems of Singular Integral Equations and Some Boundary Value Problems [Russian], Nauka, Moscow (1970). |
| [2] | Litvinchuk G. S. and Spitkovskiĭ I. M., Factorization of Matrix-Functions. Parts 1 and 2 [Russian], submitted to VINITI, no. 2410-84, Odessa (1984). |
| [3] | Adukov, V. M., Wiener-Hopf factorization of meromorphic matrix functions, St. Petersburg Math. J., 4, 51-69, (1993) · Zbl 0791.47019 |
| [4] | Gakhov, F. D., Riemann’s boundary problem for a system of n pairs of functions, Uspekhi Mat. Nauk, 7, 3-54, (1952) · Zbl 0049.05703 |
| [5] | Kiyasov, S. N., Some classes of linear conjugation problems for a three-dimensional vector that are solvable in closed form, Sib. Math. J., 56, 313-329, (2015) · Zbl 1331.30029 · doi:10.1134/S0037446615020111 |
| [6] | 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, 58-82, (2014) · Zbl 1310.47040 · doi:10.1016/j.laa.2014.06.038 |
| [7] | Gakhov, F. D., Singular cases of riemann’s boundary problem for systems of n pairs of functions, Izv. Akad. Nauk Ser. Mat., 16, 147-156, (1952) · Zbl 0048.05907 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
