The division problem for tempered distributions of one variable

We give a characterization, in one variable case, of those C∞ multipliers F such that the division problem is solvable in S (R). For these functions F ∈ OM(R) we even prove that the multiplication operator MF (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. © 2011 Elsevier Inc. All rights reserved.