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Open Access Published by De Gruyter Open Access October 17, 2013

Factorization of rational matrix functions and difference equations

J.S. Rodríguez EMAIL logo and L.F. Campos
From the journal Concrete Operators

Abstract

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.

References

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Received: 2013-03-8
Accepted: 2013-09-18
Published Online: 2013-10-17

©2013 Versita Sp. z o.o.

This content is open access.

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