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＜電子ブック＞
An Introduction to Finite Tight Frames / by Shayne F. D. Waldron
(Applied and Numerical Harmonic Analysis. ISSN:22965017)

版	1st ed. 2018.
出版者	(New York, NY : Springer New York : Imprint: Birkhäuser)
出版年	2018
本文言語	英語
大きさ	XX, 587 p. 37 illus., 12 illus. in color : online resource
著者標目	*Waldron, Shayne F. D author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Signal processing LCSH:Mathematics LCSH:Approximation theory LCSH:Harmonic analysis LCSH:Mathematical physics FREE:Fourier Analysis FREE:Signal, Speech and Image Processing FREE:Applications of Mathematics FREE:Approximations and Expansions FREE:Abstract Harmonic Analysis FREE:Mathematical Methods in Physics
一般注記	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 -- 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. Key features and topics: * First book entirely devoted to finite frames * Extensive exercises and MATLAB examples for classroom use * Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames * Later chapters delve into general theory details and recent research results * Many illustrations showing the special aspects of the geometry of finite frames * Provides an overview of the field of finite tight frames * Discusses future research directions in the field Featuring exercises and MATLAB examples in each chapter, 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4815-2

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