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Discrete frames of Poincaré coherent states in 1+3 dimensions

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Antoine, Jean-Pierre [UCL] Hohouéto, AL [UCL]

Continuous frames of coherent states of the Poincaré group in 1 + 3 dimensions P-+(up arrow) (1, 3) have been obtained previously. We address in this article the problem of discretizing (sampling) such continuous frames. The discrete frames constructed here are sets of coherent states built from compactly supported functions and the Wigner representation of the group for mass m > 0 and spin s is an element of N/2. We examine three specific examples in detail and show that tight frames may be obtained, under particular conditions, in the case of the Lorentz section.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2003
Language Anglais
Journal information "Journal of Fourier Analysis and Applications" - Vol. 9, no. 2, p. 141-173 (2003)
Peer reviewed yes
Publisher Birkhauser Boston Inc (Cambridge)
issn 1069-5869
e-issn 1531-5851
Publication status Publié
Affiliation UCL - SC/PHYS - Département de physique
Keywords coherent states ; discretization ; sampling ; frames ; Poincare group
Links
Bibliographic reference Antoine, Jean-Pierre ; Hohouéto, AL. Discrete frames of Poincaré coherent states in 1+3 dimensions. In: Journal of Fourier Analysis and Applications, Vol. 9, no. 2, p. 141-173 (2003)
Permanent URL http://hdl.handle.net/2078.1/41125