An Introduction To Frames And Riesz Bases

Author : Ole Christensen
Publisher : Birkhäuser
ISBN 13 : 3319256130
Total Pages : 704 pages
Book Rating : 4.39/5 ( download)

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Download or read book An Introduction to Frames and Riesz Bases written by Ole Christensen and published by Birkhäuser. This book was released on 2016-05-24 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005

Author : Ole Christensen
Publisher : Springer Science & Business Media
ISBN 13 : 0817646787
Total Pages : 326 pages
Book Rating : 4.83/5 ( download)

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Download or read book Frames and Bases written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2008-06-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a streamlined presentation of the author’s successful work, An Introduction to Frames and Riesz Bases, this book develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The book presents basic results in an accessible way and includes extensive exercises.

Author : Deguang Han
Publisher : American Mathematical Soc.
ISBN 13 : 0821842129
Total Pages : 314 pages
Book Rating : 4.26/5 ( download)

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Download or read book Frames for Undergraduates written by Deguang Han and published by American Mathematical Soc.. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.

Author : Peter G. Casazza
Publisher : Springer Science & Business Media
ISBN 13 : 0817683739
Total Pages : 492 pages
Book Rating : 4.33/5 ( download)

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Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.

Author : Christopher Heil
Publisher : Springer Science & Business Media
ISBN 13 : 0817646868
Total Pages : 549 pages
Book Rating : 4.68/5 ( download)

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Download or read book A Basis Theory Primer written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2011 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.

Author : Aref Jeribi
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110493861
Total Pages : 421 pages
Book Rating : 4.63/5 ( download)

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Download or read book Denseness, Bases and Frames in Banach Spaces and Applications written by Aref Jeribi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Author : Shayne F. D. Waldron
Publisher : Springer
ISBN 13 : 0817648151
Total Pages : 587 pages
Book Rating : 4.52/5 ( download)

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Download or read book An Introduction to Finite Tight Frames written by Shayne F. D. Waldron and published by Springer. This book was released on 2018-02-03 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.

Author : Ole Christensen
Publisher : Springer Science & Business Media
ISBN 13 : 0817644482
Total Pages : 166 pages
Book Rating : 4.82/5 ( download)

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Download or read book Approximation Theory written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2012-11-04 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concisely written book gives an elementary introduction to a classical area of mathematics – approximation theory – in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Featuring classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression, the book is one of the few to describe wavelets in words rather than mathematical symbols.

Author : Martin Vetterli
Publisher : Cambridge University Press
ISBN 13 : 1139916572
Total Pages : 745 pages
Book Rating : 4.78/5 ( download)

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Download or read book Foundations of Signal Processing written by Martin Vetterli and published by Cambridge University Press. This book was released on 2014-09-04 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

Author : Jelena Kovacevic
Publisher : Now Publishers Inc
ISBN 13 : 160198068X
Total Pages : 110 pages
Book Rating : 4.87/5 ( download)

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Download or read book An Introduction to Frames written by Jelena Kovacevic and published by Now Publishers Inc. This book was released on 2008 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Frames is an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox, spurred by a host of recent applications requiring some level of redundancy. It asks the question: Why and where should one use frames? And answers emphatically: Anywhere where redundancy is a must. It then goes on to discuss a host of applications that richly illustrate that answer. An Introduction to Frames is geared primarily toward engineering students and those without extensive mathematical training. It is also intended to help researchers and practitioners decide whether frames are the right tool for their application.