A method of separation of classes of linear conjugation problems for three-dimensional vector

We consider the structure of a set of piecewise-meromorphic solutions to linear conjugation problem for three-dimensional vector and its connection with solutions to a system of two problems of fractional-linear conjugation. It is shown that if there exist two piecewise-meromorphic solutions to a system of two fractional-linear conjugation problems, then a canonical system of solutions to linear conjugation problem can be constructed and a class of problems that are resolvable in closed forms can be selected.