Wavelets on Closed Subsets of the Real Line
L. Andersson · 1993
. We construct orthogonal and biorthogonal wavelets on a given closed subset of the real line. We also study wavelets satisfying certain types of boundary conditions. We introduce the concept of "wavelet probing ", which is closely related to our construction of wavelets. This technique allows us to very quickly perform a number of different numerical tasks associated with wavelets. x1. Introduction Wavelets and multiscale analysis have emerged in a number of different fields, from harmonic analysis and partial differential equations in pure mathematics to signal and image processing in computer science and electrical engineering. Typically a general function, signal, or image is broken up into linear combinations of translated and scaled versions of some simple, basic building blocks. Multiscale analysis comes with a natural hierarchical structure obtained by only considering the linear combinations of building blocks up to a certain scale. This hierarchical structure is particularly...