The Riemann problem on a finite-sheeted Riemann surface of infinite genus (Q1581454)

The paper adjoins to the author's previous investigations on Riemann boundary-value problem on Riemann surfaces [see \textit{I. A. Bikchantaev}, Math. Sb., Nov. Ser. 112(154), 256-282 (1980; Zbl 0438.30036); Izv. Vyssh. Uchebn. Zaved.., Mat. 1984, No. 9(268), 10-13 (1984; Zbl 0563.30008) and Differ. Uravn. 30, No. 5, 882-888 (1994; Zbl 0844.45003)]. The author suggests a development of his approach which enables him to give solvability conditions and an explicit solution in the general case of an arbitrary piecewise continuous contour on a finite-sheeted parabolic Riemann surface. This solution is given in terms of some analogs of Cauchy type integrals. There are given some types of contours when these integrals may be expressed via ordinary Cauchy type integrals.