Harmonic analysis : from Fourier to wavelets
 Author/Creator
 Pereyra, María Cristina.
 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
Available online

Stacks

Unknown
QA403 .P44 2012

Unknown
QA403 .P44 2012
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Contributors
 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: timefrequency 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, LittlewoodPaley theory.
 Harmonic analysis on Euclidean spaces  Nontrigonometric harmonic analysis  Wavelets and other special systems.
Bibliographic information
 Publication date
 2012
 Responsibility
 María Cristina Pereyra, Lesley A. Ward.
 Series
 Student mathematical library ; 63. IAS/Park City mathematical subseries
 ISBN
 9780821875667
 0821875663