Overview
- Exhibits several recently discovered links between traditional harmonic analysis and modern ideas in areas such as Riemannian geometry and sheaf theory
- Contains both deep theoretical results and innovative applications to various fields such as medical imagine and data science
- Only publication of its kind extending classical harmonic analysis to manifolds, graphs, and other general structures
- Comprised of original research and survey papers from well-known experts
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (17 chapters)
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Front Matter
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Introduction
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Front Matter
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Frames in Abstract Spaces
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Front Matter
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Space-Frequency Analysis in Function Spaces on Rn
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Front Matter
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Frames in Spaces of Functions on Manifolds and Groups
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Front Matter
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Keywords
About this book
The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces.
Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as:
- The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling.
- A systematic approach to shearlets with applications to wavefront sets and function spaces.
- Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions.
- Kernel methods, wavelets, and frames on compact and non-compact manifolds.
Editors and Affiliations
Bibliographic Information
Book Title: Frames and Other Bases in Abstract and Function Spaces
Book Subtitle: Novel Methods in Harmonic Analysis, Volume 1
Editors: Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-319-55550-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-55549-2Published: 22 June 2017
Softcover ISBN: 978-3-319-85692-6Published: 02 August 2018
eBook ISBN: 978-3-319-55550-8Published: 11 June 2017
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XIV, 438
Number of Illustrations: 21 b/w illustrations, 41 illustrations in colour
Topics: Abstract Harmonic Analysis, Fourier Analysis, Numerical Analysis, Big Data, Computational Science and Engineering