A CHARACTERIZATION OF WEAKLY REGULAR LINEAR FUNCTIONALS

Abstract

A linear functional is said to be weakly-regular if it is not a finite sum of Dirac masses and their derivatives. In this paper, we consider the first-order linear differential equations (Eu)'+Fu=0 where u is a non-zero linear functional and (E,F) is a pair of polynomials, with E monic. The aim of this work is to give weak-regularity conditions on u. Under certain admissibility conditions of the pair (E, F), the weak-regularity of u leads to its regularity. Some examples are analyzed.