Some convolution-type integral equations in kinetic theory (Q1569367)

The conservative Wiener-Hopf integral equation, whose kernel is an even function that is a superposition of exponential functions, is considered. A generalization of this equation is analyzed. It is proved that the limits of the solutions to these equations as \(x\) approaches \(+\infty\) exist. These limits are evaluated in terms of the Ambartsumyan function. The results are applied to problems in the kinetic theory of gases and radiative transfer theory.