The division problem for tempered distributions of one variable

Abstract

We give a characterization, in one variable case, of those C-infinity multipliers F such that the division problem is solvable in S'(R). For these functions F is an element of O-M (R) we even prove that the multiplication operator M-F(G) = FG has a continuous linear right inverse on S'(R), in contrast to what happens in the several variables case, as was shown by Langenbruch. (C) 2011 Elsevier Inc. All rights reserved.