Optimal synthesis, light scattering, and diffraction on a ribbon are
just some of the applied problems for which integral equations with
difference kernels are employed. The same equations are also met in
important mathematical problems such as inverse spectral problems,
nonlinear integral equations, and factorization of operators.
On the basis of the operator identity method, the theory of integral
operators with difference kernels is developed here, and the connection
with many applied and theoretical problems is studied. A number of
important examples are analyzed.