Frames and Other Bases in Abstract and Function Spaces Novel Methods in Harmonic Analysis, Volume 1 /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Pesenson, Isaac (Editor), Le Gia, Quoc Thong (Editor), Mayeli, Azita (Editor), Mhaskar, Hrushikesh (Editor), Zhou, Ding-Xuan (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
• Series: Applied and Numerical Harmonic Analysis,
• Subjects: Mathematics.; Harmonic analysis.; Fourier analysis.; Computer mathematics.; Numerical analysis.; Abstract Harmonic Analysis.; Fourier Analysis.; Numerical Analysis.; Big Data.; Computational Science and Engineering.

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 v...

Table of Contents:

• 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.