# Harmonic analysis : from Fourier to wavelets

- Responsibility
- María Cristina Pereyra, Lesley A. Ward.
- Language
- English.
- Imprint
- Providence, R.I. : American Mathematical Society ; Princeton, N.J. : Institute for Advanced Study, c2012.
- Physical description
- xxiv, 410 p. ; 22 cm.
- Series
- Student mathematical library ; 63. IAS/Park City mathematical subseries.

## Access

## Creators/Contributors

- Author/Creator
- Pereyra, María Cristina.
- Contributor
- Ward, Lesley A., 1963-

## Contents/Summary

- Bibliography
- Includes bibliographical references and index.
- Publisher's Summary
- 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. This book is published in cooperation with IAS/Park City Mathematics Institute.

(source: Nielsen Book Data)

## Subjects

- Subject
- Harmonic analysis > Textbooks.
- Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.)
- Harmonic analysis on Euclidean spaces -- Research exposition (monographs, survey articles)
- Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable.
- Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.
- Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems.

## Bibliographic information

- Publication date
- 2012
- Series
- Student mathematical library ; 63. IAS/Park City mathematical subseries
- ISBN
- 9780821875667 (alk. paper)
- 0821875663 (alk. paper)