The range of non-surjective convolution operators on Beurling spaces

Bonet, José ; Galbis, Antonio

Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 125-135

Résumé

Let μ ≠ 0 be an ultradistribution of Beurling type with compact support in the space . We investigate the range of the convolution operator Tμ on the space of non-quasianalytic functions of Beurling type associated with a weight w, in the case the operator is not surjective. It is proved that the range of TM always contains the space of real-analytic functions, and that it contains a smaller space of Beurling type for a weight σ ≥ ω if and only if the convolution operator is surjective on the smaller class.

Détail

DOI : 10.1017/S0017089500031335

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