Sturm-Liouville wavelets
A construction of wavelet-like functions on a compact interval of \({\mathbb R}\) is described. The approach is based on a multiscale decomposition of weighted spaces \(L_{2,p}([a,b])\), and the scaling functions are constructed with the help of eigenfunctions of regular Sturm-Liouville boundary value problems. The properties of these eigenfunctions yield stable and local bases. Corresponding fast decomposition and reconstruction algorithms are derived using DST and DCT.
scientific article; zbMATH DE number 1207279