On an application of hypoellipticity to solutions of functional equations (Q1916966)

Concerning rather general functional equations in several real variables, under conditions too extensive to reproduce here, the authors offer results which establish that all continuous (locally integrable) solutions of these equations are (almost everywhere) infinitely often differentiable. Distributions and hypoellipticity are used and theorems by \textit{H. Swiatak} [Aequationes Math. 6, 170-187 (1971; Zbl 0231.39005); Trans. Am. Math. Soc. 221, 97-118 (1976; Zbl 0333.39004)] are generalized.