On the product integration method for solving singular integral equations in scattering theory
The author considers integral equations of the form \[ K(\lambda,\mu)=A(\lambda,\mu)+\int^{\infty}_{0}\frac{A(\lambda,\eta)K( \eta,\mu)d\eta}{\mu -\eta},\quad \mu >0 \] where the integral has a Cauchy principal value. Using product integration techniques, he shows that under certain hypotheses there exists a unique solution to the equation, and constructs an approximating sequence of functions which converges to the solution. It is also shown that the integral operator involved is compact. The treatment is abstract and no examples are given.
scientific article; zbMATH DE number 4080862