The support of Mikusiński operators

Abstract

A class of Mikusiriski operators, called regular operators, is studied. The class of regular operators is strictly smaller than the class of all operators, and strictly larger than the class of all distributions with left bounded support. Regular operators have local properties. Lions' theorem of supports holds for regular operators with compact support. The fundamental solution to the Cauchy-Riemann equations is not regular, but the fundamental solution to the heat equation in two dimensions is regular and has support on a half-ray.