Artículo
Cabrelli, C.; Heil, C.; Molter, U. "Accuracy of several multidimensional refinable distributions" (2000) Journal of Fourier Analysis and Applications. 6(5):482-502
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Abstract:
Compactly supported distributions f1,..., fr on 9d are refinable if each fi is a finite linear combination of the reseated and translated distributions fj (Ax -k), where the translates k are taken along a lattice Γ ⊂ Rd and A is a dilation matrix that expansively maps Γ into itself. Refinable distributions satisfy a refinement equation f(x) = ∑k∈Λ ck f(Ax-k), where Λ is a finite subset of Γ, the ck are r × r matrices, and f = (f1,..., fr)T. The accuracy of f is the highest degree p such that all multivariate polynomials q with degree(q) < p are exactly reproduced from linear combinations of translates of f1,..., fr along the lattice Γ. We determine the accuracy p from the matrices ck. Moreover, we determine explicitly the coefficients yα,i(k) such that xα = ∑i=1 r ∑k∈Gamma; yα,i fi(x + k). These coefficients are multivariate polynomials yα,i(x) of degree |α| evaluated at lattice points k ∈ Γ. © 2000 Birkhäuser Boston. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Accuracy of several multidimensional refinable distributions |
| Autor: | Cabrelli, C.; Heil, C.; Molter, U. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón I, 1428 Buenos Aires, Argentina CONICET, Rivadavia 1917, (1033) Buenos Aires, Argentina School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States |
| Palabras clave: | Accuracy; Dilation equation; Dilation matrix; Multidimensional wavelets; Multiwavelets; Refinable distributions; Refinable functions; Refinement equation; Shift invariant spaces; Wavelets |
| Año: | 2000 |
| Volumen: | 6 |
| Número: | 5 |
| Página de inicio: | 482 |
| Página de fin: | 502 |
| Título revista: | Journal of Fourier Analysis and Applications |
| Título revista abreviado: | J. Fourier Anal. Appl. |
| ISSN: | 10695869 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli |
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Citas:
---------- APA ----------
Cabrelli, C., Heil, C. & Molter, U. (2000) . Accuracy of several multidimensional refinable distributions. Journal of Fourier Analysis and Applications, 6(5), 482-502.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli [ ]
---------- CHICAGO ----------
Cabrelli, C., Heil, C., Molter, U. "Accuracy of several multidimensional refinable distributions" . Journal of Fourier Analysis and Applications 6, no. 5 (2000) : 482-502.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli [ ]
---------- MLA ----------
Cabrelli, C., Heil, C., Molter, U. "Accuracy of several multidimensional refinable distributions" . Journal of Fourier Analysis and Applications, vol. 6, no. 5, 2000, pp. 482-502.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli [ ]
---------- VANCOUVER ----------
Cabrelli, C., Heil, C., Molter, U. Accuracy of several multidimensional refinable distributions. J. Fourier Anal. Appl. 2000;6(5):482-502.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli [ ]
