國立虎尾科技大學 |

Frames and other bases in abstract and function spaces = novel methods in harmonic analysis.. Volume 1 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Frames and other bases in abstract and function spaces/ edited by Isaac Pesenson ... [et al.].
其他題名:	novel methods in harmonic analysis.
其他作者:	Pesenson, Isaac.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xiv, 438 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Harmonic analysis. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-55550-8
ISBN:	9783319555508

Frames and other bases in abstract and function spaces = novel methods in harmonic analysis.. Volume 1 /
Frames and other bases in abstract and function spacesnovel methods in harmonic analysis.Volume 1 /[electronic resource] :edited by Isaac Pesenson ... [et al.]. - Cham :Springer International Publishing :2017. - xiv, 438 p. :ill. (some col.), digital ;24 cm. - Applied and numerical harmonic analysis,2296-5009. - Applied and numerical harmonic analysis..

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.

ISBN: 9783319555508

Standard No.: 10.1007/978-3-319-55550-8doiSubjects--Topical Terms:

672073
Harmonic analysis.

LC Class. No.: QA403

Dewey Class. No.: 515.2433

Frames and other bases in abstract and function spaces = novel methods in harmonic analysis.. Volume 1 /
LDR:04005nam a2200325 a 4500 001 905818
003 DE-He213
005 20180117153427.0
006 m d
007 cr nn 008maaau
008 190308s2017 gw s 0 eng d
020 $a 9783319555508 $q (electronic bk.)
020 $a 9783319555492 $q (paper)
024 7 $a 10.1007/978-3-319-55550-8 $2 doi
035 $a 978-3-319-55550-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA403
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.2433 $2 23
090 $a QA403 $b .F813 2017
245 0 0 $a Frames and other bases in abstract and function spaces $h [electronic resource] : $b novel methods in harmonic analysis. $n Volume 1 / $c edited by Isaac Pesenson ... [et al.].
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Birkhauser,
300 $a xiv, 438 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Applied and numerical harmonic analysis, $x 2296-5009
505 0 $a 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.
520 $a 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.
650 0 $a Harmonic analysis. $3 672073
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Abstract Harmonic Analysis. $3 672075
650 2 4 $a Fourier Analysis. $3 672627
650 2 4 $a Numerical Analysis. $3 671433
650 2 4 $a Big Data. $3 1017136
650 2 4 $a Computational Science and Engineering. $3 670319
700 1 $a Pesenson, Isaac. $3 1173231
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Applied and numerical harmonic analysis. $3 881315
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-55550-8
950 $a Mathematics and Statistics (Springer-11649)