Accuracy of several multidimensional refinable distributions
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 distri...
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| Otros Autores: | , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2000
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| Acceso en línea: | Registro en Scopus Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | 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. |
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| ISSN: | 10695869 |