Fourier Analysis And Approximation Of Functions

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Fourier Analysis And Approximation Of Functions

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Author : Roald M. Trigub
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-07

Fourier Analysis And Approximation Of Functions written by Roald M. Trigub and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.

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 And Approximation

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Author : P.L. Butzer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Fourier Analysis And Approximation written by P.L. Butzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.

Methods Of Fourier Analysis And Approximation Theory

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Author : Michael Ruzhansky
language : en
Publisher: Birkhäuser
Release Date : 2016-03-11

Methods Of Fourier Analysis And Approximation Theory written by Michael Ruzhansky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-11 with Mathematics categories.

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Fourier Analysis And Approximation Theory

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Author : György Alexits
language : en
Publisher: North-Holland
Release Date : 1978

Fourier Analysis And Approximation Theory written by György Alexits and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.

Fourier Analysis And Approximation Theory

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Author : György Alexits
language : en
Publisher:
Release Date : 1978

Fourier Analysis And Approximation Theory written by György Alexits and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Approximation theory categories.

The Gibbs Phenomenon In Fourier Analysis Splines And Wavelet Approximations

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Author : A.J. Jerri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

The Gibbs Phenomenon In Fourier Analysis Splines And Wavelet Approximations written by A.J. Jerri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Mathematical Analysis Approximation Theory And Their Applications

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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2016-06-03

Mathematical Analysis Approximation Theory And Their Applications written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Core Concepts In Real Analysis

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Author : Roshan Trivedi
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Core Concepts In Real Analysis written by Roshan Trivedi and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Core Concepts in Real Analysis" is a comprehensive book that delves into the fundamental concepts and applications of real analysis, a cornerstone of modern mathematics. Written with clarity and depth, this book serves as an essential resource for students, educators, and researchers seeking a rigorous understanding of real numbers, functions, limits, continuity, differentiation, integration, sequences, and series. The book begins by laying a solid foundation with an exploration of real numbers and their properties, including the concept of infinity and the completeness of the real number line. It then progresses to the study of functions, emphasizing the importance of continuity and differentiability in analyzing mathematical functions. One of the book's key strengths lies in its treatment of limits and convergence, providing clear explanations and intuitive examples to help readers grasp these foundational concepts. It covers topics such as sequences and series, including convergence tests and the convergence of power series. The approach to differentiation and integration is both rigorous and accessible, offering insights into the calculus of real-valued functions and its applications in various fields. It explores techniques for finding derivatives and integrals, as well as the relationship between differentiation and integration through the Fundamental Theorem of Calculus. Throughout the book, readers will encounter real-world applications of real analysis, from physics and engineering to economics and computer science. Practical examples and exercises reinforce learning and encourage critical thinking. "Core Concepts in Real Analysis" fosters a deeper appreciation for the elegance and precision of real analysis while equipping readers with the analytical tools needed to tackle complex mathematical problems. Whether used as a textbook or a reference guide, this book offers a comprehensive journey into the heart of real analysis, making it indispensable for anyone interested in mastering this foundational branch of mathematics.

Integral And Discrete Transforms With Applications And Error Analysis

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Author : Abdul Jerri
language : en
Publisher: CRC Press
Release Date : 2021-11-19

Integral And Discrete Transforms With Applications And Error Analysis written by Abdul Jerri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-19 with Mathematics categories.

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Applied Functional Analysis Approximation Methods And Computers

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Author : S.S. Kutateladze
language : en
Publisher: CRC Press
Release Date : 2010-12-12

Applied Functional Analysis Approximation Methods And Computers written by S.S. Kutateladze and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-12 with Mathematics categories.

This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.