Publications [#287146] of Ingrid Daubechies

Papers Published

1. Cohen, A; Daubechies, I; Plonka, G, Regularity of Refinable Function Vectors, Journal of Fourier Analysis and Applications, vol. 3 no. 3 (January, 1997), pp. x4-323 [doi]
   (last updated on 2026/01/14)

   Abstract:
   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.