This monograph presents the first unified exposition of generalized multiresolution analyses.
Expanding on the author's pioneering work in the field these lecture notes provide the tools
and framework for using GMRAs to extend results from classical wavelet analysis to a more
general setting. 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( n). This account of recent
developments in wavelet theory will appeal to researchers and graduate students 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.
