18/10/2012, 16:30 — 17:30 — Room P3.10, Mathematics Building
Juan Rodríguez, Universidade do Algarve
Factorization of rational matrix functions and difference equations
In the beginning of the XX century, Plemelj introduced the notion
of factorization of matrix functions. If is a
regular matrix-function on the unit circle , by (left)
factorization of relative to , we mean the
following representation: where with
, and
() is analytic and regular in
(). The matrix-function
factorization find applications in many fields like diffraction
theory, the theory of differential equations and the theory of
singular integral operators.However, only for a few classes of
matrices is known the explicit formulas for the factors of the
factorization. In our talk we will show a new method to obtain a
factorization of rational matrix-functions. The constructed method
is based on the relation between the general solution of an
homogeneous Riemann-Hilbert problem and a solution of a linear
system of difference equations with constant coefficients. We also
will provide some examples of factorization of rational matrix
function, constructed with the developed factorization procedure.