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Integral Transforms and Special Functions Volume 25, 2014 - Issue 9
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Original Articles

Radial symmetric elements and the Bargmann transform

Marco CappielloDipartimento di Matematica ‘G. Peano’, Università di Torino, Via Carlo Alberto 10, Torino, ItalyCorrespondence[email protected]
,
Luigi RodinoDipartimento di Matematica ‘G. Peano’, Università di Torino, Via Carlo Alberto 10, Torino, Italy
&
Joachim ToftDepartment of Mathematics, Linnæus University, Växjö, Sweden
Pages 756-764 | Received 13 Mar 2014, Accepted 31 Mar 2014, Published online: 07 May 2014
 
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Abstract

We prove that a function or distribution on Rd is radial symmetric, if and only if its Bargmann transform is a composition by an entire function on C and the canonical quadratic function from Cd to C.

2010 Mathematics Subject Classification:

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