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dc.contributor.author |
Wolf, K.B. |
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dc.date.accessioned |
2019-02-13T18:08:04Z |
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dc.date.available |
2019-02-13T18:08:04Z |
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dc.date.issued |
2011 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 20F28; 22E46; 33E30; 42B99; 78A05; 94A15 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2011.053 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/147171 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.
We thank the support of the Optica Matem´atica ´ projects DGAPA-UNAM IN-105008 and SEPCONACYT 79899, and we thank Guillermo Kr¨otzsch (ICF-UNAM) for his assistance with the graphics and Juvenal Rueda-Paz (Facultad de Ciencias, Universidad Aut´onoma del Estado de Morelos) for his support with the manuscript. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
The Fourier U(2) Group and Separation of Discrete Variables |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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