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...
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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147167 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Fourier Transform on Quantum Euclidean Space / K. Coulembier // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147167 |
|---|---|
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dspace |
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irk-123456789-1471672019-02-14T01:26:07Z The Fourier Transform on Quantum Euclidean Space Coulembier, K. 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. 2011 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Coulembier, K. |
| spellingShingle |
Coulembier, K. The Fourier Transform on Quantum Euclidean Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Coulembier, K. |
| author_sort |
Coulembier, K. |
| title |
The Fourier Transform on Quantum Euclidean Space |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT coulembierk thefouriertransformonquantumeuclideanspace AT coulembierk fouriertransformonquantumeuclideanspace |
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2023-05-20T17:26:46Z |
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2023-05-20T17:26:46Z |
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1796153300243972096 |