The first 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 I is organized around the theme of frames and other bases in
abstract and function spaces, covering topics such as:
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The advanced development of frames, including Sigma-Delta quantization
for fusion frames, localization of frames, and frame conditioning, as
well as applications to distributed sensor networks, Galerkin-like
representation of operators, scaling on graphs, and dynamical
sampling.
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A systematic approach to shearlets with applications to wavefront sets
and function spaces.
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Prolate and generalized prolate functions, spherical Gauss-Laguerre
basis functions, and radial basis functions.
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Kernel methods, wavelets, and frames on compact and non-compact
manifolds.
