Functional Analysis and Applications Seminar 

28/06/2005, 16:00 — 17:00 — Room P3.31, Mathematics Building
Sergei V. Rogosin, Belarussian State University, Minsk, Belarus

A nonlinear Riemann-Hilbert boundary value problem and its relation to a matrix factorization problem

We consider the relation of a particular Riemann-Hilbert boundary value problem for vector functions with matrix coefficients to a matrix factorization. Main attention is paid to the constructive solution of a matrix $C$-linear conjugation problem with piece-wise constant matrix on the plane cut along a set that consists of a finite number of intervals. The approach is based on the method of functional equations developed for the scalar case in the monograph by V.V. Mityushev and S.V. Rogosin entitled Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions. Theory and Applications, Chapman and Hall / CRC Press, 1999. The work will be published in a forthcoming paper with V.V. Mityushev.