Generalized Multiresolution Analyses

Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension functions of GMRA, wavelet sets, and generalized filters. The author's constructions of wavelet sets feature prominently, with figures to illustrate their remarkably simple geometric form. The last three chapters exhibit extensions of wavelet theory and GMRAs to other settings. These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L²(Rⁿ).

This account of recent developments in wavelet theory will appeal to researchers and graduatestudents with an interest in multiscale analysis from a pure or applied perspective. Familiarity with harmonic analysis and operator theory will be helpful to the reader, though the only prerequisite is graduate level experience with real and functional analysis.