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Generalized Multiresolution Analyses (Paperback, 1st ed. 2018)
Loot Price: R1,302
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Generalized Multiresolution Analyses (Paperback, 1st ed. 2018)
Series: Applied and Numerical Harmonic Analysis
Expected to ship within 10 - 15 working days
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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.
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