Lecture Notes in Applied and Numerical Harmonic Analysis

Generalized Multiresolution Analyses

Authors: Merrill, Kathy D.

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  • Offers the first unified treatment of generalized multiresolution analyses and wavelet theory
  • Illustrates the author’s pioneering constructions of wavelet sets
  • Facilitates an abstract understanding of wavelet sets and frames by using the GMRA formulation
  • Generalizes classical wavelet techniques in L^2(R) and beyond to abstract spaces
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  • ISBN 978-3-319-99175-7
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About this book

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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-99175-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-99174-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Multiresolution Analyses
Authors
Series Title
Lecture Notes in Applied and Numerical Harmonic Analysis
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-99175-7
DOI
10.1007/978-3-319-99175-7
Softcover ISBN
978-3-319-99174-0
Series ISSN
2512-6482
Edition Number
1
Number of Pages
X, 113
Number of Illustrations
17 b/w illustrations
Topics