Functions Of Bounded Variation And Their Fourier Transforms

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Functions of Bounded Variation and Their Fourier Transforms

Author : Elijah Liflyand
Publisher : Springer
ISBN 13 : 3030044297
Total Pages : 194 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Functions of Bounded Variation and Their Fourier Transforms by : Elijah Liflyand

Download or read book Functions of Bounded Variation and Their Fourier Transforms written by Elijah Liflyand and published by Springer. This book was released on 2019-03-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.

Bounded Variation and Around

Author : Jürgen Appell
Publisher : Walter de Gruyter
ISBN 13 : 3110265117
Total Pages : 488 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Bounded Variation and Around by : Jürgen Appell

Download or read book Bounded Variation and Around written by Jürgen Appell and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis. In the first part the basic facts about spaces of functions of bounded variation and related spaces are collected, the main ideas which are useful in studying their properties are presented, and a comparison of their importance and suitability for applications is provided, with a particular emphasis on illustrative examples and counterexamples. The second part is concerned with (sometimes quite surprising) properties of nonlinear composition and superposition operators in such spaces. Moreover, relations with Riemann-Stieltjes integrals, convergence tests for Fourier series, and applications to nonlinear integral equations are discussed. The only prerequisite for understanding this book is a modest background in real analysis, functional analysis, and operator theory. It is addressed to non-specialists who want to get an idea of the development of the theory and its applications in the last decades, as well as a glimpse of the diversity of the directions in which current research is moving. Since the authors try to take into account recent results and state several open problems, this book might also be a fruitful source of inspiration for further research.

On Fourier Series and Functions of Bounded Variation

Author : William Henry Young
Publisher :
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (963 download)

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Book Synopsis On Fourier Series and Functions of Bounded Variation by : William Henry Young

Download or read book On Fourier Series and Functions of Bounded Variation written by William Henry Young and published by . This book was released on 1913* with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fourier Transforms

Author : Salomon Bochner
Publisher : Princeton University Press
ISBN 13 : 0691095787
Total Pages : 231 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Fourier Transforms by : Salomon Bochner

Download or read book Fourier Transforms written by Salomon Bochner and published by Princeton University Press. This book was released on 1949 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of Fourier transforms from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Fourier Series of Functions of Bounded Variation

Author : David Fraser
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (433 download)

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Book Synopsis Fourier Series of Functions of Bounded Variation by : David Fraser

Download or read book Fourier Series of Functions of Bounded Variation written by David Fraser and published by . This book was released on 1973 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Theory of Functions of a Real Variable and the Theory of Fourier's Series

Author : Ernest William Hobson
Publisher :
ISBN 13 :
Total Pages : 804 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis The Theory of Functions of a Real Variable and the Theory of Fourier's Series by : Ernest William Hobson

Download or read book The Theory of Functions of a Real Variable and the Theory of Fourier's Series written by Ernest William Hobson and published by . This book was released on 1926 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation of Set-valued Functions

Author : Nira Dyn
Publisher :
ISBN 13 : 9781783263028
Total Pages : 153 pages
Book Rating : 4.2/5 (63 download)

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Book Synopsis Approximation of Set-valued Functions by : Nira Dyn

Download or read book Approximation of Set-valued Functions written by Nira Dyn and published by . This book was released on 2014 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values.

Nonlinear Analysis and Optimization

Author : Boris S. Mordukhovich
Publisher : American Mathematical Soc.
ISBN 13 : 1470417367
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Analysis and Optimization by : Boris S. Mordukhovich

Download or read book Nonlinear Analysis and Optimization written by Boris S. Mordukhovich and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

The Theory of Functions of a Real Variable and the Theory of Fourier's Series

Author : Ernest William Hobson
Publisher : CUP Archive
ISBN 13 :
Total Pages : 804 pages
Book Rating : 4./5 ( download)

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Book Synopsis The Theory of Functions of a Real Variable and the Theory of Fourier's Series by : Ernest William Hobson

Download or read book The Theory of Functions of a Real Variable and the Theory of Fourier's Series written by Ernest William Hobson and published by CUP Archive. This book was released on 1927 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lebesgue Points and Summability of Higher Dimensional Fourier Series

Author : Ferenc Weisz
Publisher : Springer Nature
ISBN 13 : 3030746364
Total Pages : 299 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Lebesgue Points and Summability of Higher Dimensional Fourier Series by : Ferenc Weisz

Download or read book Lebesgue Points and Summability of Higher Dimensional Fourier Series written by Ferenc Weisz and published by Springer Nature. This book was released on 2021-06-12 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

Proceedings of the Royal Society of London

Author : Royal Society (Great Britain)
Publisher :
ISBN 13 :
Total Pages : 706 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Proceedings of the Royal Society of London by : Royal Society (Great Britain)

Download or read book Proceedings of the Royal Society of London written by Royal Society (Great Britain) and published by . This book was released on 1911 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes research papers in the mathematical and physical sciences. Continued by: Proceedings. Mathematical and physical sciences; and, Proceedings. Mathematical, physical, and engineering sciences.

Fourier Analysis and Approximation of Functions

Author : Roald M. Trigub
Publisher : Springer Science & Business Media
ISBN 13 : 9781402023415
Total Pages : 610 pages
Book Rating : 4.0/5 (234 download)

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Book Synopsis Fourier Analysis and Approximation of Functions by : Roald M. Trigub

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.

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.

A Handbook of Fourier Theorems

Author : D. C. Champeney
Publisher : Cambridge University Press
ISBN 13 : 9780521366885
Total Pages : 206 pages
Book Rating : 4.3/5 (668 download)

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Book Synopsis A Handbook of Fourier Theorems by : D. C. Champeney

Download or read book A Handbook of Fourier Theorems written by D. C. Champeney and published by Cambridge University Press. This book was released on 1989-01-27 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented without proof in a form that is accurate but also accessible to a reader who is not a specialist mathematician. The technique of Fourier analysis has long been of fundamental importance in the physical sciences, engineering and applied mathematics, and is today of particular importance in communications theory and signal analysis. Existing books on the subject are either rigorous treatments, intended for mathematicians, or are intended for non-mathematicians, and avoid the finer points of the theory. This book bridges the gap between the two types. The text is self-contained in that it includes examples of the use of the various theorems, and any mathematical concepts not usually included in degree courses in physical sciences and engineering are explained. This handbook will be of value to postgraduates and research workers in the physical sciences and in engineering subjects, particularly communications and electronic engineering.

Functions of Generalized Bounded Variation, Generalized Absolute Continuity and Applications to Fourier Series

Author : Nunzio Paul Schembari
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (828 download)

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Book Synopsis Functions of Generalized Bounded Variation, Generalized Absolute Continuity and Applications to Fourier Series by : Nunzio Paul Schembari

Download or read book Functions of Generalized Bounded Variation, Generalized Absolute Continuity and Applications to Fourier Series written by Nunzio Paul Schembari and published by . This book was released on 1991 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tbilisi Analysis and PDE Seminar

Author : Roland Duduchava
Publisher : Springer Nature
ISBN 13 : 3031628942
Total Pages : 213 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Tbilisi Analysis and PDE Seminar by : Roland Duduchava

Download or read book Tbilisi Analysis and PDE Seminar written by Roland Duduchava and published by Springer Nature. This book was released on with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fourier Transform

Author : Salih Salih
Publisher : BoD – Books on Demand
ISBN 13 : 9535121278
Total Pages : 225 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Fourier Transform by : Salih Salih

Download or read book Fourier Transform written by Salih Salih and published by BoD – Books on Demand. This book was released on 2015-06-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of Fourier transform (FT) in signal processing and physical sciences has increased in the past decades. Almost all the textbooks on signal processing or physics have a section devoted to the FT theory. For this reason, this book focuses on signal processing and physical sciences. The book chapters are related to fast hybrid recursive FT based on Jacket matrix, acquisition algorithm for global navigation satellite system, determining the sensitivity of output parameters based on FFT, convergence of integrals of products based on Riemann-Lebesgue Lemma function, extending the real and complex number fields for treating the FT, nonmaterial structure, Gabor transform, and chalcopyrite bioleaching. The book provides applications oriented to signal processing and physics written primarily for engineers, mathematicians, physicians and graduate students, will also find it useful as a reference for their research activities.