Convolution equations on a finite interval for a class of symbols having powerlike asymptotics at infinity

A class of convolution equations is introduced on a finite interval, which is a generalization of a series of examples encountered in mathematical physics and other fields and for which a certain analogue of the Wiener–Hopf method is developed. As a corollary the Fredholm property is established for general convolution operators on a finite interval with symbols having polynomial growth at infinity in Sobolev spaces of generalized functions.
Bibliography: 31 titles.