On the solution of certain integral equations by generalized functions

Abstract

This note is concerned with a method by which generalized solutions can be shown to exist for certain types of integral equationswhere f(x) ∈ L2(0, ∞). The method is briefly this. An extended meaning is given to such equations by using generalized functions of a particular type. Then, if (1) denotes a transformation which has no everywhere-defined inverse in the usual sense, it may be possible to define in the extended sense an inverse transformationso that if f is given, a generalized function g = can be determined as a solution of (1).