Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
Novel Methods in Harmonic Analysis, Volume 2
Editors: Pesenson, I., Le Gia, Q.T., Mayeli, A., Mhaskar, H., Zhou, D.-X. (Eds.)
Free Preview- 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
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- About this book
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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 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.
- The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems.
- Table of contents (16 chapters)
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Harmonic Analysis Methods for Function Spaces, Differential Equations and Data Science
Pages 441-447
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Characterization of Gevrey Regularity by a Class of FBI Transforms
Pages 451-482
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A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems
Pages 483-516
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Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation
Pages 517-532
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Convergence and Regularization of Sampling Series
Pages 533-562
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Table of contents (16 chapters)
- Download Preface 1 PDF (22 KB)
- Download Sample pages 1 PDF (553.1 KB)
- Download Table of contents PDF (29.8 KB)
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Bibliographic Information
- Bibliographic Information
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- 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
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- Isaac Pesenson
- Quoc Thong Le Gia
- Azita Mayeli
- Hrushikesh Mhaskar
- Ding-Xuan Zhou
- Series Title
- Applied and Numerical Harmonic Analysis
- Copyright
- 2017
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-55556-0
- DOI
- 10.1007/978-3-319-55556-0
- Hardcover ISBN
- 978-3-319-55555-3
- Softcover ISBN
- 978-3-319-85693-3
- Series ISSN
- 2296-5009
- Edition Number
- 1
- Number of Pages
- XIV, 510
- Number of Illustrations
- 56 b/w illustrations, 25 illustrations in colour
- Topics
