Vol. 110, No. 1, 1984

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A class of surjective convolution operators

Wojciech Abramczuk

Vol. 110 (1984), No. 1, 1–7
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 in Rn if μ∗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 = (or 𝒟′) and = 𝒟F, 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
Authors
Wojciech Abramczuk