The Fourier Transform on Quantum Euclidean Space
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Fourier Transform on Quantum Euclidean Space
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| Creator |
Coulembier, K.
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| Description |
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.
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| Date |
2019-02-13T18:04:53Z
2019-02-13T18:04:53Z 2011 |
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| Type |
Article
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| Identifier |
The Fourier Transform on Quantum Euclidean Space / K. Coulembier // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 17B37; 81R60; 33D50 DOI:10.3842/SIGMA.2011.047 http://dspace.nbuv.gov.ua/handle/123456789/147167 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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