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

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.


42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems