Generalized Multiresolution Analyses (Applied and Numerical Harmonic Analysis) - Softcover

Buch 73 von 88: Applied and Numerical Harmonic Analysis

Merrill, Kathy D.

 
9783319991740: Generalized Multiresolution Analyses (Applied and Numerical Harmonic Analysis)
Softcover
ISBN 10: 3319991744 ISBN 13: 9783319991740
Verlag: Birkhäuser, 2018

Inhaltsangabe

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(ℝn).

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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Von der hinteren Coverseite

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(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.

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Verlag
Birkhäuser
Erscheinungsdatum
2018
Sprache
Englisch
ISBN 10 
3319991744
ISBN 13 
9783319991740
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
124
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ISBN 10:  3319991760 ISBN 13:  9783319991764
Verlag: Birkhäuser, 2018
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