Functions Of Bounded Variation And Their Fourier Transforms

Author : Elijah Liflyand
Publisher : Springer
Page : 194 pages
File Size : 41,5 Mb
Release : 2019-03-06
Category : Mathematics
ISBN : 9783030044299

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Functions of Bounded Variation and Their Fourier Transforms by Elijah Liflyand Pdf

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.

Author : Jürgen Appell,Józef Banas,Nelson José Merentes Díaz
Publisher : Walter de Gruyter
Page : 488 pages
File Size : 40,7 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9783110265118

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Bounded Variation and Around by Jürgen Appell,Józef Banas,Nelson José Merentes Díaz Pdf

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.

Author : Salomon Bochner,Komaravolu Chandrasekharan
Publisher : Princeton University Press
Page : 236 pages
File Size : 55,6 Mb
Release : 1949
Category : Mathematics
ISBN : 0691095787

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Fourier Transforms by Salomon Bochner,Komaravolu Chandrasekharan Pdf

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.

Author : Richard R. Goldberg
Publisher : Unknown
Page : 92 pages
File Size : 46,7 Mb
Release : 1961
Category : Fourier transformations
ISBN : UCBK:C037254333

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Fourier Transforms by Richard R. Goldberg Pdf

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642740299

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Classical Fourier Transforms by Komaravolu Chandrasekharan Pdf

This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener's general tauberian theorem. As an illustraiton of a Fourier transformation of a function not belonging to L1 (- , ) an integral due to Ramanujan is given. Chapter II is devoted to the L2-theory, including Plancherel's theorem, Heisenberg's inequality, the Paley-Wiener theorem, Hardy's interpolation formula and two inequalities due to Bernstein. Chapter III deals with Fourier-Stieltjes transforms. After the basic properties are explained, distribution functions, positive-definite functions and the uniqueness theorem of Offord are treated. The book is intended for undergraduate students and requires of them basic knowledge in real and complex analysis.

Author : Nira Dyn,Elza Farkhi,Alona Mokhov
Publisher : Unknown
Page : 153 pages
File Size : 53,9 Mb
Release : 2014
Category : Mathematics
ISBN : 1783263024

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Approximation of Set-valued Functions by Nira Dyn,Elza Farkhi,Alona Mokhov Pdf

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.

Author : Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 47,9 Mb
Release : 2016-02-26
Category : Game theory, economics, social and behavioral sciences
ISBN : 9781470417369

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Nonlinear Analysis and Optimization by Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski Pdf

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.

Author : Ferenc Weisz
Publisher : Springer Nature
Page : 299 pages
File Size : 40,5 Mb
Release : 2021-06-12
Category : Mathematics
ISBN : 9783030746360

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Lebesgue Points and Summability of Higher Dimensional Fourier Series by Ferenc Weisz Pdf

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.

Author : Salih Salih
Publisher : BoD – Books on Demand
Page : 225 pages
File Size : 49,6 Mb
Release : 2015-06-03
Category : Computers
ISBN : 9789535121275

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Fourier Transform by Salih Salih Pdf

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.

Author : Rajendra Bhatia
Publisher : MAA
Page : 134 pages
File Size : 48,7 Mb
Release : 2005-03-03
Category : Mathematics
ISBN : 0883857405

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Fourier Series by Rajendra Bhatia Pdf

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.

Author : R. M. Dudley,R. Norvaiša
Publisher : Springer
Page : 289 pages
File Size : 55,8 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540488149

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Differentiability of Six Operators on Nonsmooth Functions and p-Variation by R. M. Dudley,R. Norvaiša Pdf

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.

Author : Roald M. Trigub,Eduard S. Belinsky
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 51,5 Mb
Release : 2004-09-07
Category : Mathematics
ISBN : 1402023413

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Fourier Analysis and Approximation of Functions by Roald M. Trigub,Eduard S. Belinsky Pdf

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 : Ernest William Hobson
Publisher : Unknown
Page : 804 pages
File Size : 47,8 Mb
Release : 1957
Category : Fourier series
ISBN : UCLA:L0091354217

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

Author : Michael Khachay,Yury Kochetov,Panos Pardalos
Publisher : Springer
Page : 716 pages
File Size : 45,7 Mb
Release : 2019-06-12
Category : Computers
ISBN : 9783030226299

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Mathematical Optimization Theory and Operations Research by Michael Khachay,Yury Kochetov,Panos Pardalos Pdf

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.

Author : Elijah Liflyand
Publisher : Springer Nature
Page : 199 pages
File Size : 50,5 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030818920

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Harmonic Analysis on the Real Line by Elijah Liflyand Pdf

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.