The Fourier Transform on Quantum Euclidean Space
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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147167 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Fourier Transform on Quantum Euclidean Space / K. Coulembier // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147167 |
|---|---|
| record_format |
dspace |
| spelling |
Coulembier, K. 2019-02-13T18:04:53Z 2019-02-13T18:04:53Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147167 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. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html. The author would like to thank Hendrik De Bie for helpful suggestions and comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Fourier Transform on Quantum Euclidean Space Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Fourier Transform on Quantum Euclidean Space |
| spellingShingle |
The Fourier Transform on Quantum Euclidean Space Coulembier, K. |
| title_short |
The Fourier Transform on Quantum Euclidean Space |
| title_full |
The Fourier Transform on Quantum Euclidean Space |
| title_fullStr |
The Fourier Transform on Quantum Euclidean Space |
| title_full_unstemmed |
The Fourier Transform on Quantum Euclidean Space |
| title_sort |
fourier transform on quantum euclidean space |
| author |
Coulembier, K. |
| author_facet |
Coulembier, K. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147167 |
| citation_txt |
The Fourier Transform on Quantum Euclidean Space / K. Coulembier // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. |
| work_keys_str_mv |
AT coulembierk thefouriertransformonquantumeuclideanspace AT coulembierk fouriertransformonquantumeuclideanspace |
| first_indexed |
2025-11-28T07:48:18Z |
| last_indexed |
2025-11-28T07:48:18Z |
| _version_ |
1850853488469213184 |