Novel methods in harmonic analysis

✍ Scribed by Lê Gia, Quôc Thông; Mayeli, Azita; Mhaskar, Hrushikesh N.; Pesenson, Isaac; Zhou, Ding-Xuan

• Year: 2017
• Tongue: English
• Leaves: 512
• Series: Applied and numerical harmonic analysis
• Category: Library

✦ Synopsis

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

Front Matter ....Pages i-xiv
Front Matter ....Pages 439-439
Harmonic Analysis Methods for Function Spaces, Differential Equations and Data Science (Isaac Pesenson)....Pages 441-447
Front Matter ....Pages 449-449
Characterization of Gevrey Regularity by a Class of FBI Transforms (S. Berhanu, Abraham Hailu)....Pages 451-482
A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems (Hans G. Feichtinger)....Pages 483-516
Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation (Elijah Liflyand)....Pages 517-532
Convergence and Regularization of Sampling Series (W. R. Madych)....Pages 533-562
Front Matter ....Pages 563-563
Harmonic Analysis in Non-Euclidean Spaces: Theory and Application (Stephen D. Casey)....Pages 565-601
A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes (Ilwoo Cho, Palle E. T. Jorgensen)....Pages 603-651
Sheaf and Duality Methods for Analyzing Multi-Model Systems (Michael Robinson)....Pages 653-703
Front Matter ....Pages 705-705
On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operators (Praveen Agarwal, Erkinjon Karimov, Murat Mamchuev, Michael Ruzhansky)....Pages 707-718
On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators (Hussein Awala, Irina Mitrea, Katharine Ott)....Pages 719-751
On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts (Willi Freeden, Helga Nutz)....Pages 753-794
Front Matter ....Pages 795-795
An Overview of Numerical Acceleration Techniques for Nonlinear Dimension Reduction (Wojciech Czaja, Timothy Doster, Avner Halevy)....Pages 797-829
Adaptive Density Estimation on the Circle by Nearly Tight Frames (Claudio Durastanti∗)....Pages 831-860
Interactions Between Kernels, Frames, and Persistent Homology (Mijail Guillemard, Armin Iske)....Pages 861-888
Multi-Penalty Regularization for Detecting Relevant Variables (Kateřina Hlaváčková-Schindler, Valeriya Naumova, Sergiy Pereverzyev Jr.)....Pages 889-916
Stable Likelihood Computation for Gaussian Random Fields (Michael McCourt, Gregory E. Fasshauer)....Pages 917-943
Back Matter ....Pages 945-948

✦ Subjects

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