Factorization of rational matrix functions and difference equations

• Autorzy: J.S. Rodríguez , L.F. Campos
• 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.

Słowa kluczowe

EN

explicit factorization; rational matrix functions; factorization of matrix functions; Riemann-Hilbert boundary value problem; linear difference equations

Kategorie tematyczne

• 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
• 39A06: Linear equations
• 30E25: Boundary value problems

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2013
• Tom: 1
• Strony: 37-53

Daty

otrzymano

2013-03-08

zaakceptowano

2013-09-18

online

2013-10-17

Twórcy

autor

J.S. Rodríguez

• Departamento de Matemática, F.C.T., Universidade do Algarve,
  Campus de Gambelas, 8005-139 Faro, Portugal

autor

L.F. Campos

• Escola Secundária de Loulé, Avenida Laginha Serafim,
  8100-740 Loulé, Portugal

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, Advances and 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 and Applications, 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.

Identyfikatory

DOI

10.2478/conop-2012-0005