The aczel—chung equation in distributions

Abstract

In this paper we consider the functional equation

which is a generalization of the generalized D'Alembert equation (see Deeba and Koh[3]) . We will show that equation (0.1) can be reformulated into the following functional equation in distributions:

where are operators defined on D^′(I) and P is the tensor product operator for distributions. Thus equations (0.2) reduces to equation (0.1) when the solutions are regular distributions, i.e. locally Lebesgue integrable functions.

Keywords:

• Schwartz distributions,
• functional equations

MSC(1991):

• 46F10
• 39B52

Additional information

Notes on contributors

E.L. Koh

G. Ren