Multiresolution analysis, wavelets and fast algorithms on an interval. (English. Abridged French version) Zbl 0768.42015

Cohen, Albert; Daubechies, Ingrid; Jawerth, Bjorn; Vial, Pierre

C. R. Acad. Sci., Paris, Sér. I 316, No. 5, 417-421 (1993).

Summary: We adapt the standard construction of multiresolution analysis and orthonormal wavelet bases in \(L^ 2(\mathbb{R})\) to the framework of functions defined on the interval [0,1]. The main properties of wavelet bases (regularity, space localization and vanishing moments) are preserved and a fast algorithm (with a special treatment at the borders of the interval) can be derived.

MSC:

42C40

Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

multiresolution analysis; orthonormal wavelet bases; fast algorithm