We build a locally convex algebra of real analytic functions defined in a strip of the Poincaré half-plane in which a class of periodic hyperfunctions on the real line is topologically embedded. This is accomplished via a harmonic regularization method. In this algebra, we can give a sense to differential problems involving products of hyperfunctions which are a priori not defined in the classical setting. Some examples and an application are given.
"Multiplication of periodic hyperfunctions via harmonic regularization and applications." Kyoto J. Math. 59 (2) 267 - 292, June 2019. https://doi.org/10.1215/21562261-2018-0011