Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions

Making use of the pullbacks, we reformulate the following quadratic functional equation: f(x + y + z) + f(x) + f(y) + f(z) = f(x + y) + f(y + z) + f(z + x) in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperfunctions. Copyright (C) 2008 Young-Su Lee.