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OverviewThis 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. Full Product DetailsAuthor: Kathy D. MerrillPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 1st ed. 2018 Weight: 0.454kg ISBN: 9783319991740ISBN 10: 3319991744 Pages: 113 Publication Date: 12 October 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction.- The Invariance of the Core Subspace.- The Multiplicity Function.- Wavelet Sets.- Generalized Filters.- Fractal Spaces.- Composite Dilations and Crystallographic Groups.- Abstract Constructions of GMRAs.ReviewsIt is well-suited for graduate students who want to become familiar with this interesting topic and to researchers who would like to get a quick overview over the area. (Peter Massopust, zbMATH 1409.42001, 2019) This book will be appreciated mainly by graduate students and researchers, who have been already introduced to classical wavelet theory, and have interest in the development of new construction methods of wavelets, and their use in more general contexts. (Sandra Saliani, Mathematical Reviews, December, 2019) It is well-suited for graduate students who want to become familiar with this interesting topic and to researchers who would like to get a quick overview over the area. (Peter Massopust, zbMATH 1409.42001, 2019) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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