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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About this book
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science.
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 II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as:
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 II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as:
- The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems.
- Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets.
- Applications of harmonic analysis to data science and statistics
- Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
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Keywords
Table of contents (16 chapters)
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Front Matter
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Introduction
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Front Matter
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Fourier Analysis, Its Generalizations and Applications
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Front Matter
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Harmonic Analysis and Differential Equations
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Front Matter
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Editors and Affiliations
Bibliographic Information
Book Title: Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
Book Subtitle: Novel Methods in Harmonic Analysis, Volume 2
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/10.1007/978-3-319-55556-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-55555-3Published: 29 August 2017
Softcover ISBN: 978-3-319-85693-3Published: 03 August 2018
eBook ISBN: 978-3-319-55556-0Published: 09 August 2017
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XIV, 510
Number of Illustrations: 56 b/w illustrations, 25 illustrations in colour
Topics: Abstract Harmonic Analysis, Fourier Analysis, Numerical Analysis, Big Data, Computational Science and Engineering