05912nam 22007215 450 991025428390332120200629220500.03-319-55550-210.1007/978-3-319-55550-8(CKB)3710000001404653(DE-He213)978-3-319-55550-8(MiAaPQ)EBC4875428(PPN)202991512(EXLCZ)99371000000140465320170611d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierFrames and Other Bases in Abstract and Function Spaces Novel Methods in Harmonic Analysis, Volume 1 /edited by Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou1st ed. 2017.Cham :Springer International Publishing :Imprint: Birkhäuser,2017.1 online resource (XIV, 438 p. 62 illus., 41 illus. in color.) Applied and Numerical Harmonic Analysis,2296-50093-319-55549-9 Includes bibliographical references at the end of each chapters.Frames: Theory and Practice -- Dynamical Sampling and Systems from Iterative Actions of Operators -- Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling -- A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators -- Computing the Distance between Frames and between Subspaces of a Hilbert Space -- Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks -- Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings -- Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation -- A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging -- Frame Properties of Shifts of Prolate and Bandpass Prolate Functions -- Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions -- Multiscale Radial Basis Functions -- Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings -- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians -- Construction of Multiresolution Analysis Based on Localized Reproducing Kernels -- Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case -- Parseval Space-Frequency Localized Frames on Sub-Riemann Compact Homogeneous Manifolds.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.Applied and Numerical Harmonic Analysis,2296-5009Harmonic analysisFourier analysisNumerical analysisBig dataComputer mathematicsAbstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Big Datahttps://scigraph.springernature.com/ontologies/product-market-codes/I29120Computational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Harmonic analysis.Fourier analysis.Numerical analysis.Big data.Computer mathematics.Abstract Harmonic Analysis.Fourier Analysis.Numerical Analysis.Big Data.Computational Science and Engineering.515.2433Pesenson Isaacedthttp://id.loc.gov/vocabulary/relators/edtLe Gia Quoc Thongedthttp://id.loc.gov/vocabulary/relators/edtMayeli Azitaedthttp://id.loc.gov/vocabulary/relators/edtMhaskar Hrushikeshedthttp://id.loc.gov/vocabulary/relators/edtZhou Ding-Xuanedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910254283903321Frames and Other Bases in Abstract and Function Spaces1561657UNINA