Accuracy of Lattice Translates of Several Multidimensional Refinable Functions

• Autores: Cabrelli, C.; Heil, C.; Molter, U.
• Año de publicación: 1998
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: J. Approx. Theory 1998;95(1):5-52
• Materia: Accuracy; approximation by translates; dilation equations; dilation matrix; multidimensional refinable functions; multidimensional wavelets; multiwavelets; refinement equations; refinable functions; shift invariant spaces; wavelets
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.