The fundamental principle for mean-periodic distributions

Abstract

The purpose of this paper is to provide a proof for a Fundamental Principle for convolution equations μ ∗ f = 0, with μ ∈ E′(Ω) and f ∈ D′(Ω), where Ω ⊆ Rⁿ is a convex open set and E′(Ω), D′(Ω) are the corresponding distribution spaces.