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On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

Published online by Cambridge University Press:  12 July 2007

M. Belhadj  and
J. J. Betancor
M. Belhadj
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife Islas, Canarias, Spain (jbetanco@ull.es)
J. J. Betancor
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife Islas, Canarias, Spain (jbetanco@ull.es)
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Abstract

In this paper we consider Beurling-type distributions in the Hankel setting. The Hankel transform and Hankel convolution are studied on Beurling-type distributions. We also introduce a class of ultra-differential operators that allows us to show a Hankel version of the second structure theorem of Komatsu and Braun. Necessary and sufficient conditions are established in order that a Beurling distribution generates a surjective Hankel convolution operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 3 , June 2005 , pp. 479 - 512
Copyright
Copyright © Royal Society of Edinburgh 2005

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