Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, Softcover reprint of the original 1st ed. 2017 Novel Methods in Harmonic Analysis, Volume 2 Applied and Numerical Harmonic Analysis Series

Introduction.- Characterization of Gevrey Regularity by a Class of FBI Transforms.- A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems.- Asymptotic Behaviour of the Fourier Transform of a Function of Bounded Variation.- Convergence and Regularization of Sampling Series.- Harmonic Analysis in Non-Euclidean Spaces: Theory and Application.- An Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes.- Sheaf and Duality Methods for Analyzing Multi-Model Systems.- On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operator.- 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.- An Overview of Numerical Acceleration Techniques for Non-Linear 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.

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 Includes supplementary material: sn.pub/extras