Analogues of sampling theorems for some homogeneous spaces
| Autor: | Keisaku Kumahara, Masaaki Eguchi, Shin Koizumi, Mitsuhiko Ebata |
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| Rok vydání: | 2006 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Radon transform Hyperbolic space Fourier inversion theorem Mathematical analysis Lie group Sampling (statistics) Helgason-Fourier transform Integral geometry Radon Fourier reconstruction 42A99 Nyquist–Shannon sampling theorem Geometry and Topology Sampling theorem Fourier series 43A15 Analysis Mathematics |
| Zdroj: | Hiroshima Math. J. 36, no. 1 (2006), 125-140 |
| ISSN: | 0018-2079 |
| DOI: | 10.32917/hmj/1147883400 |
| Popis: | Sampling theorems are one of the basic tools in information theory. The signal function f whose band–region is contained in a certain interval can be reconstructed from their values f ðxkÞ at the sampling points fxkg. We obtain analogues of this theorem for the cases of the Fourier–Jacobi series, the complex sphere S 1 c and the complex semisimple Lie groups. And as an application of these formulae, we show a version of the sampling theorem for the Radon transform on the complex hyperbolic space. |
| Databáze: | OpenAIRE |
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