Regularity of Refinable Function Vectors

Journal Article (Journal Article)

We study the existence and regularity of compactly supported solutions φ = (φν)ν=0r- 1 of vector refinement equations. The space spanned by the translates of φν can only provide approximation order if the refinement mask P has certain particular factorization properties. We show, how the factorization of P can lead to decay of |φ̂ν(u)| as |u| →∞. The results on decay are used to prove uniqueness of solutions and convergence of the cascade algorithm.

Full Text

Duke Authors

Cited Authors

  • Cohen, A; Daubechies, I; Plonka, G

Published Date

  • January 1, 1997

Published In

Volume / Issue

  • 3 / 3

International Standard Serial Number (ISSN)

  • 1069-5869

Digital Object Identifier (DOI)

  • 10.1007/bf02649113

Citation Source

  • Scopus