Noether theorem of a kind of singular integral equation with Hilbert kernel on closed contours

摘要

We considered a kind of singular integral equation with Hilbert kernel on closed contours. By using the method of complex functions, we obtain the extended Plemelj Formula with Hilbert kernel, and based on this, we obtained the related conditions of solvability and the general solution for the characteristic singular integral equation with Hilbert kernel on closed contours.