Abstract:
Compactly supported distributions f1, . . . , fr on Rd are refinable if each fi is a finite linear combination of the rescaled 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) = ΣkεΛ 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 = Σi=1 r ΣkεΓ yα,i(k) fi(x + k). These coefficients are multivariate polynomials yα,i (x) of degree |α| evaluated at lattice points k ε Γ.
Registro:
Documento: |
Artículo
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Título: | Accuracy of Several Multidimensional Refinable Distributions |
Autor: | Cabrelli, C.; Heil, C.; Molter, U. |
Filiación: | Departamento de Matemática, Fac. 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
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Palabras clave: | Accuracy; Dilation equation; Dilation matrix; Multidimensional wavelets; Multiwavelets; Refinable distributions; Refinable functions; Refinement equation; Shift invariant spaces; Wavelets |
Año: | 2000
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Volumen: | 6
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Número: | 5
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Página de inicio: | 482
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Página de fin: | 502
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Título revista: | Journal of Knot Theory and its Ramifications
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Título revista abreviado: | J. Knot Theory Ramifications
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ISSN: | 02182165
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v6_n5_p482_Cabrelli |
Referencias:
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Citas:
---------- APA ----------
Cabrelli, C., Heil, C. & Molter, U.
(2000)
. Accuracy of Several Multidimensional Refinable Distributions. Journal of Knot Theory and its Ramifications, 6(5), 482-502.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v6_n5_p482_Cabrelli [ ]
---------- CHICAGO ----------
Cabrelli, C., Heil, C., Molter, U.
"Accuracy of Several Multidimensional Refinable Distributions"
. Journal of Knot Theory and its Ramifications 6, no. 5
(2000) : 482-502.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v6_n5_p482_Cabrelli [ ]
---------- MLA ----------
Cabrelli, C., Heil, C., Molter, U.
"Accuracy of Several Multidimensional Refinable Distributions"
. Journal of Knot Theory and its Ramifications, vol. 6, no. 5, 2000, pp. 482-502.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v6_n5_p482_Cabrelli [ ]
---------- VANCOUVER ----------
Cabrelli, C., Heil, C., Molter, U. Accuracy of Several Multidimensional Refinable Distributions. J. Knot Theory Ramifications. 2000;6(5):482-502.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182165_v6_n5_p482_Cabrelli [ ]