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

Part I. Introduction

1. Harmonic Analysis Methods for Function Spaces, Differential Equations and Data Science
Isaac Pesenson

Part II. Fourier Analysis, Its Generalizations and Applications

2. Characterization of Gevrey Regularity by a Class of FBI Transforms
S. Berhanu, Abraham Hailu

3. A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems
Hans G. Feichtinger

4. Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation
Elijah Liflyand

5. Convergence and Regularization of Sampling Series
W. R. Madych

Part III. Analysis on Non-Euclidean Spaces

6. Harmonic Analysis in Non-Euclidean Spaces: Theory and Application
Stephen D. Casey

7. A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes
Ilwoo Cho, Palle E. T. Jorgensen

8. Sheaf and Duality Methods for Analyzing Multi-Model Systems
Michael Robinson

Part IV. Harmonic Analysis and Differential Equations

9. On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operators
Praveen Agarwal, Erkinjon Karimov, Murat Mamchuev, Michael Ruzhansky

10. On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators
Hussein Awala, Irina Mitrea, Katharine Ott

11. On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts
Willi Freeden, Helga Nutz

Part V. Harmonic Analysis for Data Science

12. An Overview of Numerical Acceleration Techniques for Nonlinear Dimension Reduction
Wojciech Czaja, Timothy Doster, Avner Halevy

13. Adaptive Density Estimation on the Circle by Nearly Tight Frames
Claudio Durastanti∗

14. Interactions Between Kernels, Frames, and Persistent Homology
Mijail Guillemard, Armin Iske

15. Multi-Penalty Regularization for Detecting Relevant Variables
Kateřina Hlaváčková-Schindler, Valeriya Naumova, Sergiy Pereverzyev

16. Stable Likelihood Computation for Gaussian Random Fields
Michael McCourt, Gregory E. Fasshauer

Keywords: Mathematics, Abstract Harmonic Analysis, Fourier Analysis, Numerical Analysis, Big Data, Computational Science and Engineering