Topologies on quaternionic hyperfunctions and duality theorems

Abstract

Abstract The purpose of this paper is to establish a topological isomorphism between the space FK of H-hyperfunctions supported by a compact K and the space (G(K))′ of left H-linear functionals on G(K) space of germs of regular functions. The space FK is also topologically isomorphic to the space R ∞ 1(HP1\K) of left regular functions vanishing at infinity. We also introduce two different families of infinite order differential operators: one of them is useful to characterize the convergence in G(K) while we need the other one to write an H-hyperfunction with support at the origin as infinite sum of erivatives of Dirac's delta. Keywords: 30G3546F15