Random Fourier Series With Applications To Harmonic Analysis

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Random Fourier Series with Applications to Harmonic Analysis

Author : Michael B. Marcus
Publisher : Princeton University Press
ISBN 13 : 0691082928
Total Pages : 160 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Random Fourier Series with Applications to Harmonic Analysis by : Michael B. Marcus

Download or read book Random Fourier Series with Applications to Harmonic Analysis written by Michael B. Marcus and published by Princeton University Press. This book was released on 1981-11-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The changes to U.S. immigration law that were instituted in 1965 have led to an influx of West African immigrants to New York, creating an enclave Harlem residents now call ''Little Africa.'' These immigrants are immediately recognizable as African in their wide-sleeved robes and tasseled hats, but most native-born members of the community are unaware of the crucial role Islam plays in immigrants' lives. Zain Abdullah takes us inside the lives of these new immigrants and shows how they deal with being a double minority in a country where both blacks and Muslims are stigmatized. Dealing with this dual identity, Abdullah discovers, is extraordinarily complex. Some longtime residents embrace these immigrants and see their arrival as an opportunity to reclaim their African heritage, while others see the immigrants as scornful invaders. In turn, African immigrants often take a particularly harsh view of their new neighbors, buying into the worst stereotypes about American-born blacks being lazy and incorrigible. And while there has long been a large Muslim presence in Harlem, and residents often see Islam as a force for social good, African-born Muslims see their Islamic identity disregarded by most of their neighbors. Abdullah weaves together the stories of these African Muslims to paint a fascinating portrait of a community's efforts to carve out space for itself in a new country. -- Book jacket.

Random Fourier Series with Applications to Harmonic Analysis

Author : Michael B.. Marcus
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (491 download)

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Book Synopsis Random Fourier Series with Applications to Harmonic Analysis by : Michael B.. Marcus

Download or read book Random Fourier Series with Applications to Harmonic Analysis written by Michael B.. Marcus and published by . This book was released on 1981 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101

Author : Michael B. Marcus
Publisher : Princeton University Press
ISBN 13 : 1400881536
Total Pages : 152 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 by : Michael B. Marcus

Download or read book Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 written by Michael B. Marcus and published by Princeton University Press. This book was released on 2016-03-02 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived. The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.

Journal of Fourier Analysis and Applications Special Issue

Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 9780849315152
Total Pages : 668 pages
Book Rating : 4.3/5 (151 download)

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Book Synopsis Journal of Fourier Analysis and Applications Special Issue by : John J. Benedetto

Download or read book Journal of Fourier Analysis and Applications Special Issue written by John J. Benedetto and published by CRC Press. This book was released on 1995-09-21 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of June 1993, a Conference in Harmonic Analysis was held at the University of Paris-Sud to celebrate the role played by Jean-Pierre Kahane. The large variety of topics ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Kahane.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 510 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by : Isaac Pesenson

Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second 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 II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Handbook of Fourier Analysis & Its Applications

Author : Robert J Marks II
Publisher : Oxford University Press
ISBN 13 : 9780198044307
Total Pages : 800 pages
Book Rating : 4.0/5 (443 download)

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Book Synopsis Handbook of Fourier Analysis & Its Applications by : Robert J Marks II

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 800 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.

Excursions in Harmonic Analysis, Volume 4

Author : Radu Balan
Publisher : Birkhäuser
ISBN 13 : 3319201883
Total Pages : 428 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Excursions in Harmonic Analysis, Volume 4 by : Radu Balan

Download or read book Excursions in Harmonic Analysis, Volume 4 written by Radu Balan and published by Birkhäuser. This book was released on 2015-10-20 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Some Random Series of Functions

Author : Jean-Pierre Kahane
Publisher : Cambridge University Press
ISBN 13 : 9780521456029
Total Pages : 324 pages
Book Rating : 4.4/5 (56 download)

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Book Synopsis Some Random Series of Functions by : Jean-Pierre Kahane

Download or read book Some Random Series of Functions written by Jean-Pierre Kahane and published by Cambridge University Press. This book was released on 1985 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of Some Random Series of Functions is important and has wide application in mathematics, statistics, engineering, and physics.

Lectures on the Fourier Transform and Its Applications

Author : Brad G. Osgood
Publisher : American Mathematical Soc.
ISBN 13 : 1470441918
Total Pages : 689 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on the Fourier Transform and Its Applications by : Brad G. Osgood

Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

$\xi $-Radial Processes and Random Fourier Series

$Download $\xi $-Radial Processes and Random Fourier Series PDF Online Free$

Author : Michael B. Marcus
Publisher : American Mathematical Soc.
ISBN 13 : 0821824325
Total Pages : 193 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $\xi $-Radial Processes and Random Fourier Series by : Michael B. Marcus

Download or read book $\xi $-Radial Processes and Random Fourier Series written by Michael B. Marcus and published by American Mathematical Soc.. This book was released on 1987 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A -radial process is a stochastic process whose finite joint distributions are defined in terms of a symmetric real valued infinitely divisible random variable . This monograph is a study of the sample path continuity of a certain class of stationary stochastic processes.

Applications of Discrete and Continuous Fourier Analysis

Author : H. Joseph Weaver
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 398 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Applications of Discrete and Continuous Fourier Analysis by : H. Joseph Weaver

Download or read book Applications of Discrete and Continuous Fourier Analysis written by H. Joseph Weaver and published by Wiley-Interscience. This book was released on 1983-09 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: An applications oriented, introductory text covering the concepts and properties of Fourier Analysis. Emphasizes applications to real scientific and engineering problems. Defines the Fourier series, Fourier transform, and discrete Fourier transform. Includes over 200 illustrations.

Fourier Analysis in Probability Theory

Author : Tatsuo Kawata
Publisher : Academic Press
ISBN 13 : 148321852X
Total Pages : 681 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fourier Analysis in Probability Theory by : Tatsuo Kawata

Download or read book Fourier Analysis in Probability Theory written by Tatsuo Kawata and published by Academic Press. This book was released on 2014-06-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.

Harmonic Analysis and the Theory of Probability

Author : Salomon Bochner
Publisher : Courier Corporation
ISBN 13 : 0486446204
Total Pages : 190 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Harmonic Analysis and the Theory of Probability by : Salomon Bochner

Download or read book Harmonic Analysis and the Theory of Probability written by Salomon Bochner and published by Courier Corporation. This book was released on 2005-08-27 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis. Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; the transforms of Plancherel, Laplace, Poisson, and Mellin; applications to boundary value problems, to Dirichlet series, and to Bessel functions; and the theory of completely monotone functions. The primary significance of this text lies in the last two chapters, which offer a systematic presentation of an original concept developed by the author and partly by LeCam: Bochner's characteristic functional, a Fourier transform on a Euclidean-like space of infinitely many dimensions. The characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables, and thus constitutes an important part of progress in the theory of stochastic processes.

Harmonic Analysis on Symmetric Spaces and Applications I

Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 1461251281
Total Pages : 353 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Harmonic Analysis on Symmetric Spaces and Applications I by : Audrey Terras

Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.

Seminar on Stochastic Analysis, Random Fields and Application [sic].

Author : Robert C. Dalang
Publisher : Springer Science & Business Media
ISBN 13 : 9783764367213
Total Pages : 328 pages
Book Rating : 4.3/5 (672 download)

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Book Synopsis Seminar on Stochastic Analysis, Random Fields and Application [sic]. by : Robert C. Dalang

Download or read book Seminar on Stochastic Analysis, Random Fields and Application [sic]. written by Robert C. Dalang and published by Springer Science & Business Media. This book was released on 2002-04 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.

Commutative Harmonic Analysis IV

Author : V.P. Khavin
Publisher : Springer Science & Business Media
ISBN 13 : 3662063018
Total Pages : 235 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Commutative Harmonic Analysis IV by : V.P. Khavin

Download or read book Commutative Harmonic Analysis IV written by V.P. Khavin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: Littlewood-Paley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals.

An Introduction to Random Vibrations, Spectral & Wavelet Analysis

Author : D. E. Newland
Publisher : Courier Corporation
ISBN 13 : 0486136965
Total Pages : 514 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to Random Vibrations, Spectral & Wavelet Analysis by : D. E. Newland

Download or read book An Introduction to Random Vibrations, Spectral & Wavelet Analysis written by D. E. Newland and published by Courier Corporation. This book was released on 2012-04-03 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms. Starting with an introduction to probability distributions and averages, the text examines joint probability distributions, ensemble averages, and correlation; Fourier analysis; spectral density and excitation response relations for linear systems; transmission of random vibration; statistics of narrow band processes; and accuracy of measurements. Discussions of digital spectral analysis cover discrete Fourier transforms as well as windows and smoothing. Additional topics include the fast Fourier transform; pseudo-random processes; multidimensional spectral analysis; response of continuous linear systems to stationary random excitation; and discrete wavelet analysis. Numerous diagrams and graphs clarify the text, and complicated mathematics are simplified whenever possible. This volume is suitable for upper-level undergraduates and graduate students in engineering and the applied sciences; it is also an important resource for professionals.