Theory of a class of Wiener-Hopf equations of the first kind: Application to the Sommerfeld problem

AbstractA new theory of a class of Wiener-Hopf equations of the first kind in a space of distributions is presented. It is shown that the corresponding Wiener-Hopf operator is a Fredholm operator. This result is obtained by an appropriate modification of the standard Wiener-Hopf technique used for equations of the second kind. The nullity and defect numbers of the operator are determined from a factorization of the symbol. An application to the Sommerfeld problem is briefly considered