An Introduction to Finite Tight Frames

1. Auflage 2018
ISBN: 978-0-8176-4814-5
Verlag: Springer

Buch, Englisch, 587 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1068 g

Reihe: Applied and Numerical Harmonic Analysis

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 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.

Zielgruppe

Research

Autoren/Hrsg.

Waldron, Shayne F. D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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.- 

Über Autor(innen)

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 Wisconsin–Madison 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,