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

Author: Belhadj M.   Betancor J. J.  

Publisher: Royal Society of Edinburgh

ISSN: 1473-7124

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.135, Iss.3, 2005-06, pp. : 479-512

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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.