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The Fourier Transform on Quantum Euclidean Space
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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The Fourier Transform on Quantum Euclidean Space
Інший ID:
2010 Mathematics Subject Classification: 17B37; 81R60; 33D50
DOI:10.3842/SIGMA.2011.047
DOI:10.3842/SIGMA.2011.047
Посилання:
The Fourier Transform on Quantum Euclidean Space / K. Coulembier // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ.
Підтримка:
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.
Дата:
2011
Переглядів:
494
Завантажень:
243
Анотація:
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.
