Artículo
Cabrelli, C.A.; Molter, U.M. "Wavelet transform of the dilation equation" (1996) Journal of the Australian Mathematical Society Series B-Applied Mathematics. 37(4):474-489
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Abstract:
In this article we study the dilation equation f(x) = ∑hchf(2x-h) in ℒ2(ℝ) using a wavelet approach. We see that the structure of Multiresolution Analysis adapts very well to the study of scaling functions. The equation is reduced to an equation in a subspace of ℒ2(ℝ) of much lower resolution. This simpler equation is then "wavelet transformed" to obtain a discrete dilation equation. In particular we study the case of compactly supported solutions and we see that conditions for the existence of solutions are given by convergence of infinite products of matrices. These matrices are of the type obtained by Daubechies, and, when the analyzing wavelet is the Haar wavelet, they are exactly the same. © Australian Mathematical Society, 1996.
Registro:
| Documento: | Artículo |
| Título: | Wavelet transform of the dilation equation |
| Autor: | Cabrelli, C.A.; Molter, U.M. |
| Filiación: | Dept. de Matemática, Universidad de Buenos Aires, Pabellón I, 1428 Capital Federal, Argentina |
| Año: | 1996 |
| Volumen: | 37 |
| Número: | 4 |
| Página de inicio: | 474 |
| Página de fin: | 489 |
| Título revista: | Journal of the Australian Mathematical Society Series B-Applied Mathematics |
| ISSN: | 03342700 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03342700_v37_n4_p474_Cabrelli |
Referencias:
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- Daubechies, I., Lagarias, J.C., Sets of matrices all infinite products of which converge (1992) Linear Alg. Appl., 161, pp. 227-263
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Citas:
---------- APA ----------
Cabrelli, C.A. & Molter, U.M. (1996) . Wavelet transform of the dilation equation. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 37(4), 474-489.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03342700_v37_n4_p474_Cabrelli [ ]
---------- CHICAGO ----------
Cabrelli, C.A., Molter, U.M. "Wavelet transform of the dilation equation" . Journal of the Australian Mathematical Society Series B-Applied Mathematics 37, no. 4 (1996) : 474-489.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03342700_v37_n4_p474_Cabrelli [ ]
---------- MLA ----------
Cabrelli, C.A., Molter, U.M. "Wavelet transform of the dilation equation" . Journal of the Australian Mathematical Society Series B-Applied Mathematics, vol. 37, no. 4, 1996, pp. 474-489.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03342700_v37_n4_p474_Cabrelli [ ]
---------- VANCOUVER ----------
Cabrelli, C.A., Molter, U.M. Wavelet transform of the dilation equation. 1996;37(4):474-489.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03342700_v37_n4_p474_Cabrelli [ ]
