Effective factorization of third order Hölder matrix-functions in some classes

Abstract

We consider a homogeneous linear conjugation problem for a three-dimensional piecewise analytic vector on a simple smooth closed contour partitioning the plane of a complex variable into two regions. To each solution of the problem, we assign a triple of functions which are quotients of limiting values on the contour from the corresponding regions of the components of this solution. We provide identities relating the entries of $H$-continuous matrix function of the linear conjugation problem ensuring the existence of two of its solutions for which the corresponding components of the triples are proportional and the problem itself admits a solution in closed form.