Reflections on the q-Fourier transform and the q-Gaussian function
The standard q-Fourier Transform (qFT) of a constant diverges, which begs for a better treatment. In addition, Hilhorst has conclusively proved that the ordinary qFT is not of a one-to-one character for an infinite set of functions [H.J. Hilhorst, J. Stat. Mech. (2010) P10023]. Generalizing the ordi...
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| Autores principales: | , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/97224 https://ri.conicet.gov.ar/11336/23412 |
| Aporte de: |
| Sumario: | The standard q-Fourier Transform (qFT) of a constant diverges, which begs for a better treatment. In addition, Hilhorst has conclusively proved that the ordinary qFT is not of a one-to-one character for an infinite set of functions [H.J. Hilhorst, J. Stat. Mech. (2010) P10023]. Generalizing the ordinary qFT analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 76 (2008) 307], we appeal here to a complex q-Fourier transform, and show that the problems above mentioned are overcome. |
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