Singular Integral Equations of Convolution Type with Cosecant Kernels and Periodic Coefficients

Abstract

We study singular integral equations of convolution type with cosecant kernels and periodic coefficients in class 2 [− , ]. Such equations are transformed into a discrete jump problem or a discrete system of linear algebraic equations by using discrete Fourier transform. The conditions of Noethericity and the explicit solutions are obtained by means of the theory of classical boundary value problem and of the Fourier analysis theory. This paper will be of great significance for the study of improving and developing complex analysis, integral equations, and boundary value problems.

Generalized boundary value problems for analytic functions with convolutions and its applications

“…Thus, the results in this paper generalize the theory of the classical BVPAF and SIEs. We remark that the methods of this paper may be used to solve the above-mentioned BVPAF in Clifford analysis (see [20][21][22][23][24] ).…”

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

“…when κ < 0, (4.1) is required to fulfill. If z = ∞ is a special node, that is, μ ∞ = 0, then we can transform it into the case μ ∞ ≤ 1 2 as an ordinary node, and similar arguments can be done (see [16][17][18][19]).…”