Finite-part singular integral approximations in Hilbert spaces (Q1777802)

The authors present a finite-part singular integral equation analysis in Hilbert spaces by several approximation methods. They prove some existence theorems for the solutions of the systems of linear algebraic equations by which the finite-part singular integral equations are approximated. Later they extend the method in order to prove the existence of solutions for systems of finite-part singular integral equations, when their singularity consists of a system of diffeomorphisms of the integration interval (unit circle) on itself.