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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Introduction
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Frames in Abstract Spaces
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Space-Frequency Analysis in Function Spaces on Rn
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Frames in Spaces of Functions on Manifolds and Groups
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