On solvability of linear conjugation problem in weighted holder spaces

Abstract

For analytic vector-functions from a family of Holder spaces with a power weight at the nodes of an arbitrary piecewise-Lyapunov curve, a boundary-value problem for the linear conjugation on the curve is considered. Under the assumption that the boundary-value coefficient is a triangular matrix-function, we describe necessary and sufficient solvability conditions for that problem and provide its efficient solution