Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Novel Methods in Harmonic Analysis, Volume 2

  • Isaac Pesenson
  • Quoc Thong Le Gia
  • Azita Mayeli
  • Hrushikesh Mhaskar
  • Ding-Xuan Zhou

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

  3. Fourier Analysis, Its Generalizations and Applications

  4. Analysis on Non-Euclidean Spaces

    1. Front Matter
      Pages 563-563
  5. Harmonic Analysis and Differential Equations

    1. Front Matter
      Pages 705-705
    2. Praveen Agarwal, Erkinjon Karimov, Murat Mamchuev, Michael Ruzhansky
      Pages 707-718
  6. Harmonic Analysis for Data Science

    1. Front Matter
      Pages 795-795
    2. Wojciech Czaja, Timothy Doster, Avner Halevy
      Pages 797-829
    3. Mijail Guillemard, Armin Iske
      Pages 861-888
    4. Kateřina Hlaváčková-Schindler, Valeriya Naumova, Sergiy Pereverzyev Jr.
      Pages 889-916
    5. Michael McCourt, Gregory E. Fasshauer
      Pages 917-943
  7. Back Matter
    Pages 945-948

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.


Sampling Frames Manifolds Time-frequency Analysis Space Frequency Data Mining

Editors and affiliations

  • Isaac Pesenson
    • 1
  • Quoc Thong Le Gia
    • 2
  • Azita Mayeli
    • 3
  • Hrushikesh Mhaskar
    • 4
  • Ding-Xuan Zhou
    • 5
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA
  2. 2.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  3. 3.Department of MathematicsThe Graduate Center, CUNYNew YorkUSA
  4. 4.Institute of Mathematical SciencesClaremont Graduate UniversityClaremontUSA
  5. 5.Department of MathematicsCity University of Hong KongKowloon TongHong Kong

Bibliographic information