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The range of non-surjective convolution operators on Beurling spaces

Published online by Cambridge University Press:  18 May 2009

José Bonet  and
Antonio Galbis
José Bonet
Affiliation:
Departamento de Matemática Aplicada, E.T.S. Arquitectura, Camino de Vera, E-46071 Valencia, Spain
Antonio Galbis
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, E-46100 Burjasot (Valencia), Spain
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 125 - 135
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

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