On the solution of certain distributional boundary value problems

Abstract

The "adjoint operator method " described in [4,p.7] is used to obtain extensions of classical convolution integral operators to a class of generalised function spaces introduced by Schwartz [5]. Some general results concerning these distributional extensions are established and used to obtain solutions of certain distributional boundary/initial value problems. In the particular case where a distributional Dirichlet boundary value problem involving the Laplacian is examined, the solution obtained is shown to coincide with that derived,via a different approach, by Chaudhry and Pandey [1]