A perturbation result for surjective convolution operators on the spaces of all non-quasianalytic functions
by
David Jornet
Universidad Politécnica de Valencia

Let E_(\omega)(R^N) be the space of all non-quasianalytic functions of Beurling type on R^N. An ultradistribution \mu in E'_(\omega)(R^N) with compact support satisfies that the convolution operator f --> f*\mu is surjective in E_(\omega)(R^N) if and only if \mu is (\omega)-slowly decreasing.

We prove that if \mu is (\omega)-slowly decreasing, then \mu+\nu is also (\omega)-slowly decreasing for each \nu in E'_(\omega)(R^N) whose (\omega)-singular support does not intersect the one of \mu. The same result holds for ultradistributions of Roumieu type. This extends a result of Hörmander [2] (see also [1] for a different proof).

References

[1] W. Abramczuk, A class of surjective convolution operators, Pacific J. Math., 110 No. 1 (1984), 1-7. [2] L. Hörmander, Supports and singular supports of convolutions, Acta Math., 110 (1963), 279-302.

We report on research done under the advice of C. Fernández and A. Galbis.

(P)

Date received: April 13, 2000