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.
Keywords:matrix function, linear conjugation problem, factorization.
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