Singular integral equations of convolution type with Hilbert kernel and a discrete jump problem

Abstract

Abstract One class of singular integral equations of convolution type with Hilbert kernel is studied in the space L 2 [ − π , π ] $L^{2}[-\pi, \pi]$ in the article. Such equations can be changed into either a system of discrete equations or a discrete jump problem depending on some parameter via the discrete Laurent transform. We can thus solve the equations with an explicit representation of solutions under certain conditions.

Keywords

• singular integral equation
• convolution type
• Hilbert kernel
• a discrete jump problem