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Hankel convolution on the dual of a space of entire functions. (English) Zbl 1132.46028

The author completes the study made by himself and L. Rodríguez-Mesa [Stud. Math. 121, 35–52 (1996; Zbl 0862.46021) and Rocky Mt. J. Math. 29, 93–114 (1999; Zbl 0926.46034)], where the Hankel transform and the Hankel convolution on certain distribution spaces of exponential growth were investigated. First, he obtains new families of seminorms that generate the topology of the spaces \(X\) and \(Q\) introduced in the above papers and gives new characterizations for the pointwise multipliers of \(Q\) and for the elements of the dual space of \(Q\). The main part of the paper is dedicated to the analysis of the Hankel translation and the Hankel convolution on the spaces \(Q\) and its dual \(Q'\), establishing different characterizations for the elements in \(Q'\) which define convolution operators. Also, some algebraic properties and a distributional interchange formula for the distributional convolution are given.

MSC:

46F12 Integral transforms in distribution spaces
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