Frames And Bases

Author : Ole Christensen
Publisher : Birkhäuser
Page : 704 pages
File Size : 49,9 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9783319256139

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An Introduction to Frames and Riesz Bases by Ole Christensen Pdf

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
Page : 326 pages
File Size : 41,6 Mb
Release : 2008-06-05
Category : Mathematics
ISBN : 9780817646783

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Frames and Bases by Ole Christensen Pdf

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.
Page : 314 pages
File Size : 46,7 Mb
Release : 2007
Category : Frames (Vector analysis).
ISBN : 9780821842126

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Frames for Undergraduates by Deguang Han Pdf

"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 : Aref Jeribi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 421 pages
File Size : 52,5 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110493863

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Denseness, Bases and Frames in Banach Spaces and Applications by Aref Jeribi Pdf

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 : Ole Christensen
Publisher : Birkhäuser
Page : 313 pages
File Size : 51,7 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 0817646779

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Frames and Bases by Ole Christensen Pdf

During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing 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. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Author : Deguang Han,David R. Larson
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 46,7 Mb
Release : 2000
Category : Frames
ISBN : 9780821820674

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Frames, Bases and Group Representations by Deguang Han,David R. Larson Pdf

This work develops an operator-theoretic approach to discrete frame theory on a separable Hilbert space. It is then applied to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. Also obtained are applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.

Author : Anonim
Publisher : Unknown
Page : 336 pages
File Size : 45,7 Mb
Release : 2004
Category : Mathematics
ISBN : UCSD:31822033898388

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Memoirs of the American Mathematical Society by Anonim Pdf

Author : Peter G. Casazza,Gitta Kutyniok
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 47,6 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9780817683733

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Finite Frames by Peter G. Casazza,Gitta Kutyniok Pdf

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 : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 438 pages
File Size : 44,7 Mb
Release : 2017-06-11
Category : Mathematics
ISBN : 9783319555508

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Frames and Other Bases in Abstract and Function Spaces by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Author : Christopher Heil
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 43,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780817646868

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A Basis Theory Primer by Christopher Heil Pdf

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 : Albrecht Böttcher,Daniel Potts,Peter Stollmann,David Wenzel
Publisher : Springer
Page : 504 pages
File Size : 52,5 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9783319759968

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The Diversity and Beauty of Applied Operator Theory by Albrecht Böttcher,Daniel Potts,Peter Stollmann,David Wenzel Pdf

This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schrödinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more. The book offers researchers in operator theory open problems from applications that might stimulate their work and shows those from various applied fields, such as physics, engineering, or numerical mathematics how to use the potential of operator theory to tackle interesting practical problems.

Author : Jelena Kovacevic,Amina Chebira
Publisher : Now Publishers Inc
Page : 110 pages
File Size : 44,8 Mb
Release : 2008
Category : Computers
ISBN : 9781601980687

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An Introduction to Frames by Jelena Kovacevic,Amina Chebira Pdf

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.

Author : Verity Platt,Michael Squire
Publisher : Cambridge University Press
Page : 737 pages
File Size : 52,9 Mb
Release : 2017-04-20
Category : Art
ISBN : 9781107162365

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The Frame in Classical Art by Verity Platt,Michael Squire Pdf

This book reveals how 'marginal' aspects of Graeco-Roman art play a fundamental role in shaping and interrogating ancient and modern visual culture.

Author : Shayne F. D. Waldron
Publisher : Springer
Page : 587 pages
File Size : 43,8 Mb
Release : 2018-02-03
Category : Mathematics
ISBN : 9780817648152

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An Introduction to Finite Tight Frames by Shayne F. D. Waldron Pdf

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 : Warren W. Wiersbe
Publisher : David C Cook
Page : 13697 pages
File Size : 47,5 Mb
Release : 2023-06-09
Category : Religion
ISBN : 9780830786077

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Wiersbe Bible Commentary 2 Vol Set by Warren W. Wiersbe Pdf

The Wiersbe Bible Commentary is a must have for believers wanting a deeper and practical resource for studying God’s Word and includes: The complete Old and New Testament (Genesis to Revelation) Section-by-section commentary Biblical charts Book introductions Extended notes References Dr. Warren Wiersbe is one of the most beloved Bible teachers with over 40 years of pastoral experience. His bestselling Bible Commentaries are one of the most trustworthy resources used by pastors, Bible teachers, and persons interested in knowing more about God’s Word. His easy-to-read and insightful explanations provide a comprehensive understanding of the Bible.