Efficient Factorization in Some Classes of Second-Order Hölder Matrix Functions

A homogeneous linear conjugate problem on a closed contour for a two-dimensional piecewise analytic vector is considered. Each solution to the problem is put in correspondence to a pair of functions, which are relations of limit values on the contour of the corresponding components of this solution. The relations are specified that couple the elements of the $$H$$ -continuous matrix function of the problem, providing the existence of its two solutions, for which the corresponding components of the pair differ by rational multipliers, and the problem itself admits a solution in a closed form.