Functional equations in Schwartz distributions and their stabilities

Abstract

Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach, employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions, converting the functional equations to differential equations and find the solutions. Also we consider the Hyers-Ulam stability of the equations.