An Introduction to Finite Tight Frames, 1st ed. 2018 Applied and Numerical Harmonic Analysis Series

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing.

The first book entirely devoted to finite frames, it features extensive exercises and MATLAB examples for classroom use, important examples, and numerous illustrations. The book provides an overview of the field of finite tight frames and discusses future research directions in the field.

The book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.

Preface.- Tight Frames.- Frames.- Canonical Coordinates for Vector Spaces and Affine Spaces.- Combining and Decomposing Frames.- Variational Characterizations of Tight Frames.- The Algebraic Variet of Tight Frames.- Projective Unitary Equivalence and Fusion Frames.- Symmetries of Tight Frames.- Group Frames.- Harmonic Frames.- Equiangular and Grassmannian Frames.- Tight Frames Generated by Nonabelian Groups.- Weyl-Heisenberg SICs.- Tight Frames of Orthogonal Polynomials on the Simplex.- Continuous Tight Frames for Finite Dimensional Spaces.- Solutions.- References.- Index.-