Harmonic Analysis From Fourier to Wavelets pdf epub mobi txt 电子书下载 2025

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出版者:American Mathematical Society

作者:María Cristina Pereyra

出品人:

页数:411

译者:

出版时间:2012-6-13

价格:USD 58.00

装帧:

isbn号码:9780821875667

丛书系列:Student Mathematical Library

图书标签:

调和分析
小波
调和分析
傅里叶分析
小波分析
数学分析
函数空间
正交性
时频分析
信号处理
泛函分析
数值分析

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具体描述

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering.

In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time–frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues.

The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently.

作者简介

María Cristina Pereyra: The University of New Mexico, Albuquerque, NM,

Lesley A. Ward: University of South Australia, Mawson Lakes Campus, Adelaide, Australia

目录信息

Cover 1
Title page 4
Contents 8
List of figures 12
List of tables 14
IAS/Park City Mathematics Institute 16
Preface 18
Fourier series: Some motivation 26
Interlude: Analysis concepts 46
Pointwise convergence of Fourier series 80
Summability methods 102
Mean-square convergence of Fourier series 132
A tour of discrete Fourier and Haar analysis 152
The Fourier transform in paradise 186
Beyond paradise 214
From Fourier to wavelets, emphasizing Haar 246
Zooming properties of wavelets 286
Calculating with wavelets 328
The Hilbert transform 354
Useful tools 396
Alexander’s dragon 414
Bibliography 416
Name index 426
Subject index 428
Back Cover 437
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