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Author : Stephen S. Gelbart
Publisher : American Mathematical Soc.
ISBN 13 : 0821818082
Total Pages : 83 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fourier Analysis on Matrix Space written by Stephen S. Gelbart and published by American Mathematical Soc.. This book was released on 1971 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stephen Gelbart
Publisher :
ISBN 13 :
Total Pages : 77 pages
Book Rating : 4.:/5 (559 download)
Download or read book Fourier Analysis on Matrix Space. Gelbart written by Stephen Gelbart and published by . This book was released on 1971 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stephen S. Gelbart
Publisher :
ISBN 13 : 9780608091778
Total Pages : 81 pages
Book Rating : 4.0/5 (917 download)
Download or read book Fourier Analysis on Matrix Space written by Stephen S. Gelbart and published by . This book was released on with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher : Cambridge University Press
ISBN 13 : 9780521457187
Total Pages : 456 pages
Book Rating : 4.4/5 (571 download)
Download or read book Fourier Analysis on Finite Groups and Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 1999-03-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Author : Jayakumar Ramanathan
Publisher : Springer Science & Business Media
ISBN 13 : 1461217563
Total Pages : 334 pages
Book Rating : 4.4/5 (612 download)
Download or read book Methods of Applied Fourier Analysis written by Jayakumar Ramanathan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Adrian Constantin
Publisher : Cambridge University Press
ISBN 13 : 1316670805
Total Pages : 368 pages
Book Rating : 4.3/5 (166 download)
Download or read book Fourier Analysis: Volume 1, Theory written by Adrian Constantin and published by Cambridge University Press. This book was released on 2016-05-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.
Author : Tim Hsu
Publisher : American Mathematical Soc.
ISBN 13 : 147045145X
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)
Download or read book Fourier Series, Fourier Transforms, and Function Spaces: A Second Course in Analysis written by Tim Hsu and published by American Mathematical Soc.. This book was released on 2020-02-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Series, Fourier Transforms, and Function Spaces is designed as a textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces, allowing for both a deeper and more elegant approach. This approach also allows junior and senior undergraduates to study topics like PDEs, quantum mechanics, and signal processing in a rigorous manner. Students interested in statistics (time series), machine learning (kernel methods), mathematical physics (quantum mechanics), or electrical engineering (signal processing) will find this book useful. With 400 problems, many of which guide readers in developing key theoretical concepts themselves, this text can also be adapted to self-study or an inquiry-based approach. Finally, of course, this text can also serve as motivation and preparation for students going on to further study in analysis.
Author : Gerlind Plonka
Publisher : Springer Nature
ISBN 13 : 3031350057
Total Pages : 676 pages
Book Rating : 4.0/5 (313 download)
Download or read book Numerical Fourier Analysis written by Gerlind Plonka and published by Springer Nature. This book was released on 2023-11-08 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Author : S. Allen Broughton
Publisher : John Wiley & Sons
ISBN 13 : 1118211006
Total Pages : 266 pages
Book Rating : 4.1/5 (182 download)
Download or read book Discrete Fourier Analysis and Wavelets written by S. Allen Broughton and published by John Wiley & Sons. This book was released on 2011-10-13 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough guide to the classical and contemporary mathematical methods of modern signal and image processing Discrete Fourier Analysis and Wavelets presents a thorough introduction to the mathematical foundations of signal and image processing. Key concepts and applications are addressed in a thought-provoking manner and are implemented using vector, matrix, and linear algebra methods. With a balanced focus on mathematical theory and computational techniques, this self-contained book equips readers with the essential knowledge needed to transition smoothly from mathematical models to practical digital data applications. The book first establishes a complete vector space and matrix framework for analyzing signals and images. Classical methods such as the discrete Fourier transform, the discrete cosine transform, and their application to JPEG compression are outlined followed by coverage of the Fourier series and the general theory of inner product spaces and orthogonal bases. The book then addresses convolution, filtering, and windowing techniques for signals and images. Finally, modern approaches are introduced, including wavelets and the theory of filter banks as a means of understanding the multiscale localized analysis underlying the JPEG 2000 compression standard. Throughout the book, examples using image compression demonstrate how mathematical theory translates into application. Additional applications such as progressive transmission of images, image denoising, spectrographic analysis, and edge detection are discussed. Each chapter provides a series of exercises as well as a MATLAB project that allows readers to apply mathematical concepts to solving real problems. Additional MATLAB routines are available via the book's related Web site. With its insightful treatment of the underlying mathematics in image compression and signal processing, Discrete Fourier Analysis and Wavelets is an ideal book for mathematics, engineering, and computer science courses at the upper-undergraduate and beginning graduate levels. It is also a valuable resource for mathematicians, engineers, and other practitioners who would like to learn more about the relevance of mathematics in digital data processing.
Author : Steven L. Brunton
Publisher : Cambridge University Press
ISBN 13 : 1009098489
Total Pages : 615 pages
Book Rating : 4.0/5 (9 download)
Download or read book Data-Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author : S. Nanda
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9788173196027
Total Pages : 234 pages
Book Rating : 4.1/5 (96 download)
Download or read book Sequences, Summability and Fourier Analysis written by S. Nanda and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Köthe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Nörlund summability.
Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 140088389X
Total Pages : 312 pages
Book Rating : 4.4/5 (8 download)
Download or read book Introduction to Fourier Analysis on Euclidean Spaces (PMS-32), Volume 32 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author : Bao Luong
Publisher : Springer Science & Business Media
ISBN 13 : 0817649166
Total Pages : 167 pages
Book Rating : 4.8/5 (176 download)
Download or read book Fourier Analysis on Finite Abelian Groups written by Bao Luong and published by Springer Science & Business Media. This book was released on 2009-08-14 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.
Author : William O. Bray
Publisher : CRC Press
ISBN 13 : 1000153681
Total Pages : 468 pages
Book Rating : 4.0/5 (1 download)
Download or read book Fourier Analysis written by William O. Bray and published by CRC Press. This book was released on 2020-12-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
Author : Roald M. Trigub
Publisher : Springer Science & Business Media
ISBN 13 : 9781402023415
Total Pages : 610 pages
Book Rating : 4.0/5 (234 download)
Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.
Author : Yutaka Yamamoto
Publisher : SIAM
ISBN 13 : 9781611972313
Total Pages : 282 pages
Book Rating : 4.9/5 (723 download)
Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigor. From Vector Spaces to Function Spaces presents: an easily accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.
Author : Robert J Marks II
Publisher : Oxford University Press
ISBN 13 : 0198044305
Total Pages : 799 pages
Book Rating : 4.1/5 (98 download)
Download or read book Handbook of Fourier Analysis & Its Applications written by Robert J Marks II and published by Oxford University Press. This book was released on 2009-01-08 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.
