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Harmonic Analysis: From Fourier to Wavelets
María Cristina Pereyra, Lesley A Ward
Price : ₹ 1140.00  
ISBN : 978-1-4704-2564-7
Language : English
Pages : 436
Binding : Paperback
Book Size : 140 x 216 mm
Year : 2016
Series : American Mathematical Society
Territorial Rights : Restricted
Imprint : No Image

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About the Book

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

Table of Contents

List of figures 
List of tables IAS/Park City Mathematics Institute 
Suggestions for instructors 
Chapter 1. Fourier series: Some motivation  
Chapter 2. Interlude: Analysis concepts 
Chapter 3. Pointwise convergence of Fourier series 
Chapter 4. Summability methods 
Chapter 5. Mean-square convergence of Fourier series 
Chapter 6. A tour of discrete Fourier and Haar analysis 
Chapter 7. The Fourier transform in paradise 
Chapter 8. Beyond paradise 
Chapter 9. From Fourier to wavelets, emphasizing Haar 
Chapter 10. Zooming properties of wavelets 
Chapter 11. Calculating with wavelets 
Chapter 12. The Hilbert transform 
Appendix. Useful tools 
Name index 
Subject index

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

María Cristina Pereyra is Professor at the Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA.

Lesley A Ward is Associate Professor of Mathematics at the School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes Campus, Adelaide, Australia.