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The fourier transform on quantum euclidean space

Kevin Coulembier UGent (2011) SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 7.
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
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
DIFFERENTIAL-CALCULUS, HARMONIC-OSCILLATOR, SCHRODINGER-EQUATION, Q-EXPONENTIALS, Q-INTEGRATION, POLYNOMIALS, U-Q(SO(N)), LAGUERRE, ALGEBRA, SOQ(N), quantum Euclidean space, Fourier transform, q-Hankel transform, harmonic analysis, q-polynomials, harmonic oscillator
journal title
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Symmetry Integr. Geom.
volume
7
article number
047
pages
27 pages
Web of Science type
Article
Web of Science id
000290429100001
JCR category
PHYSICS, MATHEMATICAL
JCR impact factor
1.071 (2011)
JCR rank
33/55 (2011)
JCR quartile
3 (2011)
ISSN
1815-0659
DOI
10.3842/SIGMA.2011.047
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1246386
handle
http://hdl.handle.net/1854/LU-1246386
date created
2011-05-29 08:50:55
date last changed
2016-12-21 15:42:20
@article{1246386,
  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},
  articleno    = {047},
  author       = {Coulembier, Kevin},
  issn         = {1815-0659},
  journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
  keyword      = {DIFFERENTIAL-CALCULUS,HARMONIC-OSCILLATOR,SCHRODINGER-EQUATION,Q-EXPONENTIALS,Q-INTEGRATION,POLYNOMIALS,U-Q(SO(N)),LAGUERRE,ALGEBRA,SOQ(N),quantum Euclidean space,Fourier transform,q-Hankel transform,harmonic analysis,q-polynomials,harmonic oscillator},
  language     = {eng},
  pages        = {27},
  title        = {The fourier transform on quantum euclidean space},
  url          = {http://dx.doi.org/10.3842/SIGMA.2011.047},
  volume       = {7},
  year         = {2011},
}

Chicago
Coulembier, Kevin. 2011. “The Fourier Transform on Quantum Euclidean Space.” Symmetry Integrability and Geometry-methods and Applications 7.
APA
Coulembier, Kevin. (2011). The fourier transform on quantum euclidean space. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 7.
Vancouver
1.
Coulembier K. The fourier transform on quantum euclidean space. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2011;7.
MLA
Coulembier, Kevin. “The Fourier Transform on Quantum Euclidean Space.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 7 (2011): n. pag. Print.