An Introduction to Finite Tight Frames

The theory and applications of finite tight frames has developed rapidly in recent years. This text offers an overview of the field and discusses future research directions. It includes exercises, MATLAB examples for classroom use, and numerous illustrations.

First book entirely devoted to finite frames

Replete with exercises, illustrations, and MATLAB examples

Well suited as a textbook for a graduate course or seminar on finite frames

Real-world applications to signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing

For a broad readership in pure and applied mathematics, engineering, mathematical physics, and signal processing

First book entirely devoted to finite frames Replete with exercises, illustrations, and MATLAB examples Well suited as a textbook for a graduate course or seminar on finite frames Real-world applications to signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing For a broad readership in pure and applied mathematics, engineering, mathematical physics, and signal processing

Autorentext
Shayne Waldron is a senior lecturer in the Mathematics Department of the University of Auckland. He received his Ph.D. in Mathematics from the University of WisconsinMadison and served as a postdoctoral fellow at the Israel Institute of Technology. His areas of research include approximation theory and numerical analysis and the construction of tight frames from abstract groups,

Inhalt

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.-