Advertisement

Russian Mathematics

, Volume 63, Issue 6, pp 19–28 | Cite as

Some Classes of Linear Conjugation Problems for a Four-Dimensional Vector That Are Solvable in Closed Form

  • S. N. KiyasovEmail author
Article
  • 5 Downloads

Abstract

We consider the structure of the set of piecewise meromorphic solutions of 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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vekua, N.P. Systems of Singular Integral Equations and Some Boundary Problems (Nauka, Moscow, 1970) [in Russain].Google Scholar
  2. 2.
    Litvinchuk, G.S., Spitkovskii, I.M. Factorization of Matrix-functions, Parts I, II, Available from VINITI, 17.04.84, No 2410-84 (AN USSR, Odessa, 1984).Google Scholar
  3. 3.
    Adukov, V.M. “Wiener-Hopf Factorization of Piecewise Meromorphic Matrix Functions”, Sb. Math. 200 (7-8), 1105–1126 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gahov, F.D. “Riemann’s Boundary Problem for a System of n Pairs of Functions”, Uspehi Matem. Nauk (N.S.) 7 (4), 3–54 (1952).MathSciNetGoogle Scholar
  5. 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, 58–82 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kiyasov, S.N. “On an Addition to the General Theory of the Linear Conjugation Problem for a Piecewise Analytic Vector”, Sib. Math. J. 59 (2), 288–294 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gahov, F.D. “Singular Cases of Riemann’s Boundary Problem for Systems of n Pairs of Functions”, Izvestiya Akad. Nauk SSSR. Ser. Mat. 16 (2), 147–156 (1952).MathSciNetGoogle Scholar
  8. 8.
    Kiyasov, S.N. “Some Classes of Linear Conjugation Problems for a Three-dimensional Vector that are Solvable in Closed Form”, Sib. Math. J. 56 (2), 313–329 (2015).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

Personalised recommendations