Hankel convolution operators on entire functions and distributions
type: Item
instance of: scholarly article
title: Hankel convolution operators on entire functions and distributions
zbMATH Open document ID: 1012.44003
DOI: 10.1016/S0022-247X(02)00350-5
author: Mohamed Belhadj
author: Jorge J. Betancor
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The Hankel transformation \(\varphi\to h_\mu (\varphi)\) of order \(\mu>-1/2\) is defined here as: \[ h_\mu (\varphi)(x)= \int^\infty_0 (xy)^{-\mu} J_\mu(xy) \varphi(y)y^{2\mu+1} dy\;(x<0), \] where \(J_\mu\) is the Bessel function of the first kind and order \(\mu\). The Hankel convolution \(f,g\to f*g\) is defined such that \(h_\mu (f*g)= h_\mu(f) h_\mu(g)\). The authors study Hankel convolution operators on the space of even and entire functions and on distribution spaces and prove that they are hypercyclic and chaotic. The Hankel convolution operators are characterized as those operators commuting with the Hankel translations or, equivalently, with the Bessel operator \(\Delta_\mu= z^{-2\mu-1} Dz^{2\mu+1}D\).
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 1866730
zbMATH Keywords: Hankel transformation
zbMATH Keywords: Hankel convolution operators
zbMATH Keywords: entire functions
zbMATH Keywords: distribution spaces
zbMATH Keywords: Hankel translations
zbMATH Keywords: Bessel operator
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866730