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Certain classes of problems on linear conjugation for a two-dimensional vector admitting explicit solutions

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Abstract

We consider the structure of the set of piecewise meromorphic solutions to the linear conjugation problem for a two-dimensional vector and study its relations with the fractional-linear conjugation problem. We prove that under the assumption of the piecewise meromorphic solvability of any of these problems there exists a canonical system of solutions to the linear conjugation problem and describe classes of problems which are solvable in a closed form.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008, Russia

    S. N. Kiyasov

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  1. S. N. Kiyasov
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Correspondence to S. N. Kiyasov.

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Original Russian Text © S.N. Kiyasov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 1, pp. 3–20.

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Kiyasov, S.N. Certain classes of problems on linear conjugation for a two-dimensional vector admitting explicit solutions. Russ Math. 57, 1–16 (2013). https://doi.org/10.3103/S1066369X13010015

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  • DOI: https://doi.org/10.3103/S1066369X13010015

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