Regularity of Refinable Function Vectors

We study the existence and regularity of compactly supported solutions φ = (φν)ν=0^{r- 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.

Duke Scholars

Author Ingrid Daubechies Mathematics