A class of surjective convolution operators

Wojciech Abramczuk

Vol. 110 (1984), No. 1, 1–7

DOI: 10.2140/pjm.1984.110.1

Abstract

Let μ be a distribution with compact support in Rⁿ. In the terminology of Ehrenpreis [2] μ is called invertible for a space of distributions ℱ in Rⁿ if μ∗ℱ = ℱ. Using his characterisation of invertible distributions in terms of the growth of their Fourier transforms, we obtain a class of invertible distributions which properly contains the distributions with finite supports. We consider ℱ = ℰ (or 𝒟′) and ℱ = 𝒟_F′, but our results for the latter space are only partial.

Mathematical Subject Classification 2000

Primary: 46F10

Secondary: 47B99

Milestones

Received: 7 April 1982

Published: 1 January 1984