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Open Access Green as soon as Postprint is submitted to ZB.
On a Convolution Property Characterizing the Laguerre Functions.
Monatsh. Math. 107, 281-285 (1989)
Consider the Laguerre functionslpn(t)=(−1)n2p−−√Ln(2pt)e−pt (with parameterp>0), where theL n are the Laguerre polynomials with parameter α=0.{l n p (t)} n=0 ∞ forms a complete orthonormal system inL 2 ([0, ∞)). A well known and often used property of the Laguerre functions is the convolution property:2p−−√lpi∗lpj=lpi+j+lpi+j+1 for alli,j≥0. It is the objectiveof this note that the system of Laguerre functions is the only complete and orthonormal system ofL 2 ([0, ∞)) satisfying the convolution property.
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Publication type
Article: Journal article
Document type
Scientific Article
ISSN (print) / ISBN
0026-9255
Journal
Monatshefte für Mathematik
Quellenangaben
Volume: 107,
Pages: 281-285
Publisher
Universität Wien
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)