Multicomplex Hyperfunctions and Multicomplex Microfunctions

Abstract

In this paper, we develop a theory of multicomplex hyperfunctions. Applying functorial techniques, we introduce the notion of multicomplex hyperfunctions of several variables and establish their idempotent representation theorem. Additionally, we provide a microlocal study of multicomplex hyperfunctions, in which we define the notion of multicomplex microfunctions and prove some of their fundamental properties.