Fourier Analysis And Approximation Volume 1 One Dimensional Theory
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Fourier Analysis And Approximation Volume 1 One Dimensional Theory
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Author : PL. BUTZER
language : en
Publisher:
Release Date : 1971
Fourier Analysis And Approximation Volume 1 One Dimensional Theory written by PL. BUTZER and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
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.
Handbook Of Fourier Analysis Its Applications
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Author : Robert J. Marks
language : en
Publisher: Oxford University Press
Release Date : 2009-01-08
Handbook Of Fourier Analysis Its Applications written by Robert J. Marks and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-08 with Mathematics categories.
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.
Numerical Fourier Analysis
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Author : Gerlind Plonka
language : en
Publisher: Springer Nature
Release Date : 2023-11-08
Numerical Fourier Analysis written by Gerlind Plonka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Fast And Approximate Computation Of Laplace And Fourier Transforms
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Author : Ines Melzer
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2016-03-20
Fast And Approximate Computation Of Laplace And Fourier Transforms written by Ines Melzer and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-20 with Mathematics categories.
In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments.
Fourier Analysis And Approximation Vol 1
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Author : Paul Leo Butzer
language : en
Publisher:
Release Date : 1971
Fourier Analysis And Approximation Vol 1 written by Paul Leo Butzer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Measure And Integration Theory On Infinite Dimensional Spaces
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Author :
language : en
Publisher: Academic Press
Release Date : 1972-10-16
Measure And Integration Theory On Infinite Dimensional Spaces written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-10-16 with Mathematics categories.
Measure and Integration Theory on Infinite-Dimensional Spaces
Proceedings Of The Third International Colloquium On Numerical Analysis
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Author : D. Bainov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Proceedings Of The Third International Colloquium On Numerical Analysis written by D. Bainov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "Proceedings of the Third International Colloquium on Numerical Analysis".
Harmonic Analysis On The Real Line
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Author : Elijah Liflyand
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Harmonic Analysis On The Real Line written by Elijah Liflyand and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
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.
Fourier Meets Hilbert And Riesz
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Author : René Erlin Castillo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-07-05
Fourier Meets Hilbert And Riesz written by René Erlin Castillo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-05 with Mathematics categories.
This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms. Ideal for self-study or a one semester course in Fourier analysis, included are detailed examples and exercises.