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.