The Fourier U(2) Group and Separation of Discrete Variables
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Fourier U(2) Group and Separation of Discrete Variables
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| Creator |
Wolf, K.B.
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| Description |
The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R), whose maximal compact subgroup is the Fourier group U(2)F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4). Two distinct subalgebra chains are used to model arrays of N² points placed along Cartesian or polar (radius and angle) coordinates, thus realizing one case of separation in two discrete coordinates. The N2-vectors in this space are digital (pixellated) images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.
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| Date |
2019-02-13T18:08:04Z
2019-02-13T18:08:04Z 2011 |
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| Type |
Article
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| Identifier |
The Fourier U(2) Group and Separation of Discrete Variables / K.B. Wolf, L.E. Vicent // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 20F28; 22E46; 33E30; 42B99; 78A05; 94A15 DOI:10.3842/SIGMA.2011.053 http://dspace.nbuv.gov.ua/handle/123456789/147171 |
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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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