Frames and Other Bases in Abstract and Function Spaces

Part I. Introduction

1. Frames: Theory and Practice
Isaac Pesenson

Part II. Frames in Abstract Spaces

2. Dynamical Sampling and Systems from Iterative Actions of Operators
Akram Aldroubi, Armenak Petrosyan

3. Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling
Radu Balan, Matthew Begué, Chae Clark, Kasso Okoudjou

4. A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators
Peter Balazs, Karlheinz Gröchenig

5. Computing the Distance Between Frames and Between Subspaces of a Hilbert Space
Travis Bemrose, Peter G. Casazza, Desai Cheng, John Haas, Hanh Nguyen

6. Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks
Jiayi Jiang, Alexander M. Powell

Part III. Space-Frequency Analysis in Function Spaces on Rn

7. Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
Giovanni S. Alberti, Stephan Dahlke, Filippo Mari, Ernesto Vito, Hartmut Führ

8. Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation
Amara Ammari, Tahar Moumni, Ahmed Zayed

9. A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging
John J. Benedetto, Alfredo Nava-Tudela, Alexander M. Powell, Yang Wang

10. Frame Properties of Shifts of Prolate and Bandpass Prolate Functions
Jeffrey A. Hogan, Joseph D. Lakey

11. Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions
Jürgen Prestin, Christian Wülker

12. Multiscale Radial Basis Functions
Holger Wendland

Part IV. Frames in Spaces of Functions on Manifold and Groups

13. Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings
Swanhild Bernstein, Paul Keydel

14. Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
Anna Breger, Martin Ehler, Manuel Gräf

15. Construction of Multiresolution Analysis Based on Localized Reproducing Kernels
K. Nowak, M. Pap

16. Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case
Vignon S. Oussa

17. Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds
Isaac Pesenson

Keywords: Mathematics, Abstract Harmonic Analysis, Fourier Analysis, Numerical Analysis, Big Data, Computational Science and Engineering