On a functional equation of Aczél and Chung
The equation in the title, the locally integrable solutions of which have been determined in [Studia Sci. Math. Hungar. 17, 51-67 (1982; Zbl 0553.39005)] is \((*)\) \(\sum^ m_{j=0}F_ j(a_ jx+b_ jy)=\sum^ n_{k=1}G_ k(x)H_ k(y)\). The author solves the analogue of this equation for (Laurent Schwartz) distributions by first reducing it to the case where \(m=1\). This can be done because distributions are differentiable and, by applying \(b_ pD_ x-a_ pD_ y\) to \((*)\) \((D_ x\) and \(D_ y\) are the derivations with respect to \(x\) or \(y\), respectively), one gets a similar equation with (by 1) lower \(m\).
scientific article; zbMATH DE number 493237
scientific article