Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
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 equa...
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| Autores principales: | , , |
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| Formato: | Artículo publishedVersion |
| Publicado: |
1998
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00219045_v95_n1_p5_Cabrelli https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00219045_v95_n1_p5_Cabrelli_oai |
| Aporte de: |
| Sumario: | 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. |
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