Pesenson I., Le Gia Q.T., Mayeli A., Mhaskar H., Zhou D.-X. (Eds.) Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science. Volume 2: Novel Methods in Harmonic Analysis

Springer International Publishing AG, 2017. — 512 p. — (Applied and Numerical Harmonic Analysis) — ISBN: 3319555553.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.
Contents to Volume IIFourier Analysis, Its Generalizations and Applications
Characterization of Gevrey Regularity by a Class of FBI Transforms
A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems
Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation
Convergence and Regularization of Sampling Series
Analysis on Non-Euclidean Spaces
Harmonic Analysis in Non-Euclidean Spaces: Theory and Application
A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes
Sheaf and Duality Methods for Analyzing Multi-Model Systems
Harmonic Analysis and Differential Equations
On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operators
On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators
On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts
Harmonic Analysis for Data Science
An Overview of Numerical Acceleration Techniques for Nonlinear Dimension Reduction
Adaptive Density Estimation on the Circle by Nearly Tight Frames
Interactions Between Kernels, Frames, and Persistent Homology
Multi-Penalty Regularization for Detecting Relevant Variables
Stable Likelihood Computation for Gaussian Random Fields
Contents to Volume IFrames: Theory and Practice
Frames in Abstract Spaces
Dynamical Sampling and Systems from Iterative Actions of Operators
Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling
A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators
Computing the Distance Between Frames and Between Subspaces of a Hilbert Space
Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks.
Space-Frequency Analysis in Function Spaces on Rn
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation
A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging
Frame Properties of Shifts of Prolate and Bandpass Prolate Functions
Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions
Multiscale Radial Basis Functions
Frames in Spaces of Functions on Manifolds and Groups
Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings
Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
Construction of Multiresolution Analysis Based on Localized Reproducing Kernels
Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case
Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds