Accuracy of several multidimensional refinable distributions

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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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Detalles Bibliográficos
Autor principal: Cabrelli, C.
Otros Autores: Heil, C., Molter, U.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2000
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a Cabrelli, C. 
245 1 0 |a Accuracy of several multidimensional refinable distributions 
260 |c 2000 
270 1 0 |m Cabrelli, C.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón I, 1428 Buenos Aires, Argentina; email: ccabrell@dm.uba.ar 
506 |2 openaire  |e Política editorial 
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504 |a De Boor, C., Ron, A., The exponentials in the span of the integer translates of a compactly supported function (1992) J. London Math. Soc., 45, pp. 519-535 
504 |a De Boor, C., De Vore, R., Ron, A., Approximation from shift-invariant subspaces of L2(Rd) (1994) Trans. Am. Math. Soc., 341, pp. 787-806 
504 |a Cabrelli, C., Heil, C., Molter, U., Accuracy of lattice translates of several multidimensional refinable functions (1998) J. Approx. Th., 95, pp. 5-52 
504 |a Cabrelli, C., Heil, C., Molter, U., (1999) Self-similarity and Multiwavelets in Higher Dimensions, , preprint 
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504 |a Han, B., Jia, R.-Q., Multivariate refinement equations and subdivision schemes (1998) SIAM J. Math. Anal., 29, pp. 1177-1199 
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504 |a Jia, R.-Q., The subdivision and transition operators associated with a refinement equation (1996) Advanced Topics in Multivariate Approximation, (Montecatini Terme, 1995), pp. 139-154. , Fontanella, F., Jetter, K., and Laurent, P.-J., Eds., World Scientific, River Edge, NJ 
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504 |a Jia, R.-Q., Riemenschneider, S.D., Zhou, D.X., Approximation by multiple refinable functions (1997) Canad. J. Math., 49, pp. 944-962 
504 |a Jiang, Q., Multivariate matrix refinable functions with arbitrary matrix dilation (1999) Trans. Am. Math. Soc., 351, pp. 2407-2438 
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520 3 |a 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.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón I, 1428 Buenos Aires, Argentina 
593 |a CONICET, Rivadavia 1917, (1033) Buenos Aires, Argentina 
593 |a School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States 
690 1 0 |a ACCURACY 
690 1 0 |a DILATION EQUATION 
690 1 0 |a DILATION MATRIX 
690 1 0 |a MULTIDIMENSIONAL WAVELETS 
690 1 0 |a MULTIWAVELETS 
690 1 0 |a REFINABLE DISTRIBUTIONS 
690 1 0 |a REFINABLE FUNCTIONS 
690 1 0 |a REFINEMENT EQUATION 
690 1 0 |a SHIFT INVARIANT SPACES 
690 1 0 |a WAVELETS 
700 1 |a Heil, C. 
700 1 |a Molter, U. 
773 0 |d 2000  |g v. 6  |h pp. 482-502  |k n. 5  |p J. Fourier Anal. Appl.  |x 10695869  |t Journal of Fourier Analysis and Applications 
856 4 1 |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-23044522973&partnerID=40&md5=bb23e4af42c8fc27e81fcbd744c69bb3  |y Registro en Scopus 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_10695869_v6_n5_p482_Cabrelli  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v6_n5_p482_Cabrelli  |y Registro en la Biblioteca Digital 
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962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 63125 

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