Integral Equations With Difference Kernels On Finite Intervals Ii

Integral Equations with Difference Kernels on Finite Intervals

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.

Integral Equations with Difference Kernels on Finite Intervals II

In this memorandum the authors present a technique for the solution of certain integral equations, on a finite interval of the real line, that arise in the theories of neutron transport, radiative transfer, and linearized gas dynamics. The kernels in the equations studied are functions of the difference of the arguments and involve an exponential factor. By the methods of singular integral equations, the result for the resolvent kernel is obtained in the form of simple quadratures and rapidly convergent Fredholmequations. (Author).

Integral Equations with Difference Kernels on Finite Intervals