Sturm-Liouville Wavelets

Abstract

In this paper, we describe a new construction of wavelet-like functions on a compact interval [a, b] C ℝ. Our approach of localizing multiscale decomposition of weighted L2-spaces L2,ρ([a, b]) is based on eigenfunctions of regular Sturm-Liouville boundary value problems, and was introduced and analyzed in Depczynski (1995). The asymptotic properties of such eigenfunctions yield localizing and stable bases, which prove to be very useful in time-frequency analysis. For specific types of eigenfunctions, fast algorithms are presented. © 1998 Academic Press.