Table of contents
About this book
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:
- 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.
- A systematic approach to shearlets with applications to wavefront sets and function spaces.
- Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions.
- Kernel methods, wavelets, and frames on compact and non-compact manifolds.
Sampling Frames Manifolds Time-frequency Analysis Space Frequency Data Mining
Editors and affiliations
- DOI https://doi.org/10.1007/978-3-319-55550-8
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-55549-2
- Online ISBN 978-3-319-55550-8
- Series Print ISSN 2296-5009
- Series Online ISSN 2296-5017
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