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Factorization of rational matrix functions and difference equations

100%

Rodríguez J. S., Campos L. F.

Concrete Operators

2013

tom 1

37-53

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.

Toeplitz operators and Wiener-Hopf factorisation: an introduction

100%

Câmara M. C.

Concrete Operators

2017

tom 4

nr 1

130-145

Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)

Ograniczanie wyników

2 Concrete Operators

1 Campos L. F.

1 Câmara M. C.

1 Rodríguez J. S.

1 2017

1 2013

Wyniki wyszukiwania

Factorization of rational matrix functions and difference equations

Toeplitz operators and Wiener-Hopf factorisation: an introduction