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Abstract:

Complex-valued functionsf1,...,fronRdarerefinableif they are linear combinations of finitely many of the rescaled and translated functionsfi(Ax-k), where the translateskare taken along a latticeΓ⊂RdandAis adilation matrixthat expansively mapsΓinto itself. Refinable functions satisfy arefinement equationf(x)=∑k∈Λckf(Ax-k), whereΛis a finite subset ofΓ, theckarer×rmatrices, andf(x)=(f1(x),...,fr(x))T. Theaccuracyoffis the highest degreepsuch that all multivariate polynomialsqwith degree(q)<pare exactly reproduced from linear combinations of translates off1,...,fralong the latticeΓ. In this paper, we determine the accuracypfrom the matricesck. Moreover, we determine explicitly the coefficientsyα,i(k) such thatxα=∑ri=1∑ k∈Γyα,i(k)fi(x+k). These coefficients are multivariate polynomialsyα,i(x) of degree α evaluated at lattice pointsk∈1. © 1998 Academic Press.

Registro:

Documento: Artículo
Título:Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
Autor:Cabrelli, C.; Heil, C.; Molter, U.
Filiación:School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States
Departamento de Matemática, Fac. de Ciencias Exactas Y Naturales, Univ. de Buenos Aires, Cd. Univ., Pabellón I, 1428, Buenos Aires, Argentina
Palabras clave:Accuracy; approximation by translates; dilation equations; dilation matrix; multidimensional refinable functions; multidimensional wavelets; multiwavelets; refinement equations; refinable functions; shift invariant spaces; wavelets
Año:1998
Volumen:95
Número:1
Página de inicio:5
Página de fin:52
DOI: http://dx.doi.org/10.1006/jath.1997.3211
Título revista:Journal of Approximation Theory
Título revista abreviado:J. Approx. Theory
ISSN:00219045
CODEN:JAXTA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00219045_v95_n1_p5_Cabrelli.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v95_n1_p5_Cabrelli

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Citas:

---------- APA ----------
Cabrelli, C., Heil, C. & Molter, U. (1998) . Accuracy of Lattice Translates of Several Multidimensional Refinable Functions. Journal of Approximation Theory, 95(1), 5-52.
http://dx.doi.org/10.1006/jath.1997.3211
---------- CHICAGO ----------
Cabrelli, C., Heil, C., Molter, U. "Accuracy of Lattice Translates of Several Multidimensional Refinable Functions" . Journal of Approximation Theory 95, no. 1 (1998) : 5-52.
http://dx.doi.org/10.1006/jath.1997.3211
---------- MLA ----------
Cabrelli, C., Heil, C., Molter, U. "Accuracy of Lattice Translates of Several Multidimensional Refinable Functions" . Journal of Approximation Theory, vol. 95, no. 1, 1998, pp. 5-52.
http://dx.doi.org/10.1006/jath.1997.3211
---------- VANCOUVER ----------
Cabrelli, C., Heil, C., Molter, U. Accuracy of Lattice Translates of Several Multidimensional Refinable Functions. J. Approx. Theory. 1998;95(1):5-52.
http://dx.doi.org/10.1006/jath.1997.3211