Treffer: Some functional equations in the spaces of generalized functions

The authors consider some classical functional equations (Cauchy, Pexider, Jensen, D'Alembert, quadratic) in the spaces of generalized functions such as the Schwartz distributions and the Sato hyperfunctions. These equations written for the functions from \(\mathbb{R}^n\) to \(\mathbb{C}\) themselves make no sense in the spaces of generalized functions. The authors extend these functional equations to the spaces of generalized functions making use of the tensor product and pullback of generalized functions as in \textit{S.-Y. Chung's} paper [ibid. 59, 108--123 (2000; Zbl 0945.39013)]. These extended functional equations are solved in the spaces of tempered distributions and Fourier hyperfunctions. In the final part of the paper the authors study also the ``nonhomogeneous'' additive functional equation.