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Applied and Numerical Harmonic Analysis

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.)

    • 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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eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-55556-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-319-55555-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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 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.



Table of contents (16 chapters)

  • Harmonic Analysis Methods for Function Spaces, Differential Equations and Data Science

    Pesenson, Isaac

    Pages 441-447

  • Characterization of Gevrey Regularity by a Class of FBI Transforms

    Berhanu, S. (et al.)

    Pages 451-482

  • A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems

    Feichtinger, Hans G.

    Pages 483-516

  • Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation

    Liflyand, Elijah

    Pages 517-532

  • Convergence and Regularization of Sampling Series

    Madych, W. R.

    Pages 533-562

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-55556-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-319-55555-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
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
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XIV, 510
Number of Illustrations and Tables
56 b/w illustrations, 25 illustrations in colour
Topics