An Introduction to Finite Tight Frames

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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,

Zusammenfassung

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

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.-

Details

Erscheinungsjahr:	2019
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Applied and Numerical Harmonic Analysis
Inhalt:	xx 587 S. 25 s/w Illustr. 12 farbige Illustr. 587 p. 37 illus. 12 illus. in color.
ISBN-13:	9781493979202
ISBN-10:	1493979205
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Waldron, Shayne F. D.
Auflage:	Softcover reprint of the original 1st ed. 2018
Hersteller:	Springer New York Springer US, New York, N.Y. Applied and Numerical Harmonic Analysis
Maße:	235 x 155 x 33 mm
Von/Mit:	Shayne F. D. Waldron
Erscheinungsdatum:	04.06.2019
Gewicht:	0,908 kg

Artikel-ID: 115188816