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2013 | 1 | 37-53
Tytuł artykułu

Factorization of rational matrix functions and difference equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the beginning of the twentieth century, Plemelj introduced the notion of factorization of matrix functions. The matrix factorization finds applications in many fields such as in the diffraction theory, in the theory of differential equations and in the theory of singular integral operators. However, the explicit formulas for the factors of the factorization are known only in a few classes of matrices. In the present paper we consider a new approach to obtain the factorization of a rational matrix function, relative to the unit circle. The constructed method is based on the relation between the general solution of a homogeneous Riemann-Hilbert problem and a solution of a linear system of difference equations with constant coefficients.
Wydawca
Czasopismo
Rocznik
Tom
1
Strony
37-53
Opis fizyczny
Daty
otrzymano
2013-03-08
zaakceptowano
2013-09-18
online
2013-10-17
Twórcy
  • Departamento de Matemática, F.C.T., Universidade do Algarve,
    Campus de Gambelas, 8005-139 Faro, Portugal, jsanchez@ualg.pt
autor
Bibliografia
  • [1] H. Bart, I. Gohberg, M. A. Kaashoek, Minimal Factorization of Matrix and Operator Functions. Birkhäuser, 1979.
  • [2] K. F. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators. Birkhäuser, 1981.
  • [3] I. Gohberg, M. A. Kaashoek and I. M. Spitkovsky, An Overview of Matrix Factorization. Operator Theory, Advancesand Applications, Vol. 141, 1-102,Birkhäuser, 2003[WoS]
  • [4] S. E. Elaydi, An Introduction to Difference Equations. Springer, 1999.
  • [5] G. S. Litvinchuk and I. M. Spitkovskii, Factorization of Measurable Matrix Functions. Operator Theory, Advances andApplications, Vol. 25, Birkhäuser, 1987.
  • [6] M. J. Morgado, Factorization of Rational Matrix Functions. University of Algarve, Portugal, 2006. (in portuguese)
  • [7] N. I. Muskhelishvili, Sigular Integral Equations. Dover Publications, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_conop-2012-0005
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