Diffraction and Dirchlet problem for parameter-elliptic convolution operators with constant symbols

Abstract

In this paper we evaluate the difference between the inverse operators of a Dirichlet problem and of a diffraction problem for parameter-elliptic convolution operators with constant symbols. We prove that the inverse operator of a Dirichlet problem can be obtained as a limit case of such a diffraction problem.

Quaestiones Mathematicae 28(2005), 337–353.