Abstract.
In this paper, we present a general solution of the scalar Riemann problem on a closed Riemann surface in the case of a compound contour in the class of piecewise meromorphic functions multiple of a given divisor. All the results are known and belong to the author [15–17], except for the existence theorems and properties of basic functionals and also properties of a θ-function. The solution of the problem in a ‘special case’ has been announced by the author but not published [15]. Similar problems and some applications are considered in [1, 2, 12].
The main results of the paper were obtained by the author during his collaboration with Professor G. S. Litvinchuk, and this paper is devoted to his cherished memory.
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Received: April 13, 2007. Accepted: June 13, 2008.
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Zverovich, E.I. The Problem of Linear Conjugation on a Closed Riemann Surface. Complex anal.oper. theory 2, 709–732 (2008). https://doi.org/10.1007/s11785-008-0082-x
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DOI: https://doi.org/10.1007/s11785-008-0082-x