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Applied and Numerical Harmonic Analysis

Frames and Other Bases in Abstract and Function Spaces

Novel Methods in Harmonic Analysis, Volume 1

Editors: Pesenson, I., Le Gia, Q.T., Mayeli, A., Mhaskar, H., Zhou, D.-X. (Eds.)

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    • 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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  • ISBN 978-3-319-55550-8
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Softcover $149.99
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  • ISBN 978-3-319-85692-6
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About this book

The first 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 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.

Table of contents (17 chapters)

Table of contents (17 chapters)
  • Frames: Theory and Practice

    Pages 3-12

    Pesenson, Isaac

  • Dynamical Sampling and Systems from Iterative Actions of Operators

    Pages 15-26

    Aldroubi, Akram (et al.)

  • Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling

    Pages 27-45

    Balan, Radu (et al.)

  • A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators

    Pages 47-79

    Balazs, Peter (et al.)

  • Computing the Distance Between Frames and Between Subspaces of a Hilbert Space

    Pages 81-99

    Bemrose, Travis (et al.)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-55550-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-55549-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-3-319-85692-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-55550-8
DOI
10.1007/978-3-319-55550-8
Hardcover ISBN
978-3-319-55549-2
Softcover ISBN
978-3-319-85692-6
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XIV, 438
Number of Illustrations
21 b/w illustrations, 41 illustrations in colour
Topics

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