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 : 224 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 224 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.

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.

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.

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:

Classical Fourier Analysis

Author : Loukas Grafakos
Publisher : Springer Science & Business Media
ISBN 13 : 0387094326
Total Pages : 494 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Classical Fourier Analysis by : Loukas Grafakos

Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online

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.

Decay of the Fourier Transform

Author : Alex Iosevich
Publisher : Springer
ISBN 13 : 3034806256
Total Pages : 226 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Decay of the Fourier Transform by : Alex Iosevich

Download or read book Decay of the Fourier Transform written by Alex Iosevich and published by Springer. This book was released on 2014-10-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.

Harmonic Analysis and Partial Differential Equations

Author : Anatoly Golberg
Publisher : Springer Nature
ISBN 13 : 3031254244
Total Pages : 319 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Harmonic Analysis and Partial Differential Equations by : Anatoly Golberg

Download or read book Harmonic Analysis and Partial Differential Equations written by Anatoly Golberg and published by Springer Nature. This book was released on 2023-04-26 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Fourier Series

Author : Rajendra Bhatia
Publisher : MAA
ISBN 13 : 9780883857403
Total Pages : 134 pages
Book Rating : 4.8/5 (574 download)

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Book Synopsis Fourier Series by : Rajendra Bhatia

Download or read book Fourier Series written by Rajendra Bhatia and published by MAA. This book was released on 2005-03-03 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, or to supplement undergraduate courses on mathematical analysis. Beginning with a brief summary of the rich history of the subject over three centuries, the reader will appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory then provides unforeseen applications in diverse areas. Exercises of varying difficulty are included throughout to test understanding. A broad range of applications are also covered, and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students.

Differentiability of Six Operators on Nonsmooth Functions and p-Variation

Author : R. M. Dudley
Publisher : Springer
ISBN 13 : 3540488146
Total Pages : 289 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Differentiability of Six Operators on Nonsmooth Functions and p-Variation by : R. M. Dudley

Download or read book Differentiability of Six Operators on Nonsmooth Functions and p-Variation written by R. M. Dudley and published by Springer. This book was released on 2006-12-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Mathematical Optimization Theory and Operations Research

Author : Michael Khachay
Publisher : Springer
ISBN 13 : 3030226298
Total Pages : 742 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Mathematical Optimization Theory and Operations Research by : Michael Khachay

Download or read book Mathematical Optimization Theory and Operations Research written by Michael Khachay and published by Springer. This book was released on 2019-06-12 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 48 full papers presented in this volume were carefully reviewed and selected from 170 submissions. MOTOR 2019 is a successor of the well-known International and All-Russian conference series, which were organized in Ural, Siberia, and the Far East for a long time. The selected papers are organized in the following topical sections: mathematical programming; bi-level optimization; integer programming; combinatorial optimization; optimal control and approximation; data mining and computational geometry; games and mathematical economics.

Proceedings of the London Mathematical Society

Author : London Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 588 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Proceedings of the London Mathematical Society by : London Mathematical Society

Download or read book Proceedings of the London Mathematical Society written by London Mathematical Society and published by . This book was released on 1913 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Papers presented to J. E. Littlewood on his 80th birthday" issued as 3d ser., v. 14 A, 1965.

Functions of Bounded Variation

Author : Simon Reinwand
Publisher : Cuvillier Verlag
ISBN 13 : 373696403X
Total Pages : 336 pages
Book Rating : 4.7/5 (369 download)

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Book Synopsis Functions of Bounded Variation by : Simon Reinwand

Download or read book Functions of Bounded Variation written by Simon Reinwand and published by Cuvillier Verlag. This book was released on 2021-04-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions of bounded variation are most important in many fields of mathe¬matics. This thesis investigates spaces of functions of bounded variation with one variable of various types, compares them to other classical function spaces and reveals natural “habitats” of BV-functions. New and almost comprehensive results concerning mapping properties like surjectivity and injectivity, several kinds of continuity and compactness of both linear and nonlinear operators bet¬ween such spaces are given. A new theory about different types of convergence of sequences of such operators is presented in full detail and applied to a new proof for the continuity of the composition operator in the classical BV-space. The abstract results serve as ingredients to solve Hammerstein and Volterra in¬tegral equations using fixed point theory. Many criteria guaranteeing the exis¬tence and uniqueness of solutions in BV-type spaces are given and later applied to solve boundary and initial value problems in a nonclassical setting. A big emphasis is put on a clear and detailed discussion. Many pictures and syn¬optic tables help to visualize and summarize the most important ideas. Over 160 examples and counterexamples illustrate the many abstract results and how de¬licate some of them are.

Harmonic Analysis on the Real Line

Author : Elijah Liflyand
Publisher : Springer Nature
ISBN 13 : 3030818926
Total Pages : 199 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Harmonic Analysis on the Real Line by : Elijah Liflyand

Download or read book Harmonic Analysis on the Real Line written by Elijah Liflyand and published by Springer Nature. This book was released on 2021-09-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.