Abstract:
A homogeneous linear conjugate problem on a closed contour for a two-dimensional piecewise analytic vector is considered. Each solution of the problem is given a pair of functions, which are relations of limit values on the contour of the corresponding components of this solution. The relations connecting the elements of the $H$-continuous matrix-functions 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 closed form, are specified.
Keywords:matrix-function, linear conjugation problem, factorization.
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