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Approximation theory --- 517.518.8 --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Approximation of functions by polynomials and their generalizations --- 517.518.8 Approximation of functions by polynomials and their generalizations

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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.

Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Fourier analysis. --- Computer mathematics. --- Numerical analysis. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Numerical Analysis. --- Big Data. --- Computational Science and Engineering. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Big data. --- Computer science. --- Informatics --- Science --- Data sets, Large --- Large data sets --- Data sets --- Analysis, Fourier --- Computer mathematics --- Electronic data processing

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Harmonic analysis. Fourier analysis --- Mathematical analysis --- Numerical analysis --- Computer science --- Information systems --- Fourieranalyse --- analyse (wiskunde) --- Fourierreeksen --- computers --- informatica --- mathematische modellen --- wiskunde --- gegevensanalyse --- informaticaonderzoek --- computerkunde --- numerieke analyse