The method of stable completion in the classical wavelet context (Q849429)

The construction of biorthogonal wavelet bases is addressed with the method of stable completion introduced by \textit{J. M. Carnicer, W. Dahmen} and \textit{J. M. Peña} [Appl. Comput. Harmon. Anal. 3, No. 2, 127--153 (1996; Zbl 0859.42025)]. The author shows that the method of stable completion, using a special initial stable completion, for compactly supported biorthogonal scaling functions, delivers up to scaling and shifting the same biorthogonal wavelets as in [\textit{A. Cohen, I. Daubechies} and \textit{J.-C. Feauveau}, Commun. Pure Appl. Math. 45, No. 5, 485--560 (1992; Zbl 0776.42020)].