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Accuracy of Lattice Translates of Several Multidimensional Refinable Functions

Cabrelli, C. - Heil, C. - Molter, U.
   
Fecha:
1998
Tipo de documento: 
info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion
Formato:
application/pdf
Temas:
Accuracy; approximation by translates; dilation equations; dilation matrix; multidimensional refinable functions; multidimensional wavelets; multiwavelets; refinement equations; refinable functions; shift invariant spaces; wavelets
Descripción:
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.
Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente:
J. Approx. Theory 1998;95(1):5-52
Identificador:
http://hdl.handle.net/20.500.12110/paper_00219045_v95_n1_p5_Cabrelli
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00219045_v95_n1_p5_Cabrelli_oai
Derechos:
info:eu-repo/semantics/openAccess

Cita bibliográfica:

Cabrelli, C. ; Heil, C. ; Molter, U.  (1998).  Accuracy of Lattice Translates of Several Multidimensional Refinable Functions.  (info:eu-repo/semantics/article).  [consultado:  ] Disponible en el Repositorio Digital Institucional de la Universidad de Buenos Aires:  <http://hdl.handle.net/20.500.12110/paper_00219045_v95_n1_p5_Cabrelli>