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Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
dc.contributor.author | Guerrero García, Julio | |
dc.contributor.author | Sánchez Monreal, Juan Carlos | |
dc.contributor.author | Calixto Molina, Manuel | |
dc.date.accessioned | 2008-10-29T08:25:36Z | |
dc.date.available | 2008-10-29T08:25:36Z | |
dc.date.issued | 2008-04 | |
dc.identifier.citation | CALIXTO MOLINA, Manuel, GUERRERO GARCÍA, Julio, SÁNCHEZ MONREAL, Juan Carlos. Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere. Journal of Fourier Analysis and Applications, 14 (4): 538-567, Abril 2008. ISSN 1069-5869 | es |
dc.identifier.issn | 1069-5869 | |
dc.description.abstract | Using coherent-state techniques, we prove a sampling theorem for Majorana’s (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to J, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform. | es |
dc.description.sponsorship | Work partially supported by the MCYT and Fundación Séneca under projects FIS2005-05736-C03-01 and 03100/PI/05. | es |
dc.format | application/pdf | |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.title | Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere | es |
dc.type | info:eu-repo/semantics/article | es |
dc.subject.other | Matemática Aplicada | es |
dc.subject | Transformacion rápida de Fourier | es |
dc.subject | Esferas Riemann | es |
dc.subject | Armónicos esféricos | es |
dc.subject | Funciones Majorana | es |
dc.subject | Matrices circulantes | es |
dc.subject | Matrices rectangulares de Fourier | es |
dc.identifier.uri | http://hdl.handle.net/10317/525 | |
dc.identifier.uri | arXiv:math-ph/0612046v1 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess |
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