On q-analogues of the Fourier and Hankel transforms
By Tom H. Koornwinder, Rene F. Swarttouw. 2012
229 citations recorded by the source corpus.
For H. Exton's q-analogue of the Bessel function (going back to W. Hahn in a special case, but different from F. H. Jackson's q-Bessel functions) we derive Hansen-Lommel type orthogonality relations, which, by a symmetry, turn out to be equivalent to orthogonality relations which are q-analogues of the Hankel integral transform pair. These results are implicit, in the context of quantum groups, in a paper by Vaksman and Korogodskii. As a specialization we get q-cosines and q-sines which admit q-analogues of the Fourier-cosine and Fourier-sine transforms
Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Organic Chemistry
View Paper: https://www.semanticscholar.org/paper/b3ec8f2fb0ff29dec405737058fba185a25b196d
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In Applied Mathematics
In Atomic and Molecular Physics, and Optics
In Organic Chemistry
Citations in the corpus
- A q-sampling theorem related to the q-Hankel transform (2004, methodology): “MR95j:33050 [8] T. H. Koornwinder, R. F. Swarttouw, On q-analogues of the Fourier and Hankel transforms.”
- The Mellin Transform in Quantum Calculus (2006, background): “The third q-Bessel function (see [6], [ 12 ]) is given, and is denoted by M. E. H. Ismail as”
- The history of q-calculus and a new method (2000, methodology): “Exton’s q-analogue of the Bessel function we derive Hansen-Lommel type orthogonality relations, which, by a symmetry, turn out to be equivalent to orthogonality relations which are q-analogues of the Hankel integral transform pair [533].”