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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 047, 30 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.047
(Mi sigma605)
 

This article is cited in 3 scientific papers (total in 3 papers)

The Fourier Transform on Quantum Euclidean Space

Kevin Coulembier

Gent University, Galglaan 2, 9000 Gent, Belgium
Full-text PDF (570 kB) Citations (3)
References:
Abstract: We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of $q$-Hankel transforms using the first and second $q$-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
Keywords: quantum Euclidean space; Fourier transform; $q$-Hankel transform; harmonic analysis; $q$-polynomials; harmonic oscillator.
Received: November 19, 2010; in final form April 21, 2011; Published online May 11, 2011
Bibliographic databases:
Document Type: Article
MSC: 17B37; 81R60; 33D50
Language: English
Citation: Kevin Coulembier, “The Fourier Transform on Quantum Euclidean Space”, SIGMA, 7 (2011), 047, 30 pp.
Citation in format AMSBIB
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\by Kevin Coulembier
\paper The Fourier Transform on Quantum Euclidean Space
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\totalpages 30
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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