The solvability of a kind of generalized Riemann–Hilbert problems on function spaces \(H_{\ast }\)

[摘要] In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain general solutions and conditions of solvability on function spaces $H_{\ast }$ . At the end of this paper, we consider in detail the behavior of the solution at ∞ and in different domains. Thus the results in this paper generalize and improve the theory of the classical Riemann–Hilbert problems.

[学科分类] 电力

[关键词] Riemann–Hilbert problems;Singular integral equations;Sokhotski–Plemelj formula;Canonical function;Function spaces \(H_{\ast }\)