Stability of an additive functional equation in the spaces of generalized functions

Abstract

We reformulate the following additive functional equation with n-independent variablesas the equation for the spaces of generalized functions. Making use of the fundamental solution of the heat equation we solve the general solutions and the stability problems of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the regularizing functions, we extend these results to the space of distributions. 2000 MSC: 39B82; 46F05.