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020			_a9781470425647
040			_aNISER LIBRARY _cNISER LIBRARY _beng
082	0	0	_a517.57 _bPER-H
100	1		_aPereyra, María Cristina.
245	1	0	_aHarmonic analysis : _bfrom fourier to wavelets
260			_aHyderabad : _bUniversities Press, _c2016
300			_axxix, 410 p. : _bill. ; _c23 cm.
490	0		_aStudent mathematical library ; _aIAS/Park City mathematical subseries _vvolume 63.
504			_aIncludes bibliographical references (p. 391-399) and index.
520			_aIn 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.
521			_aUndergraduate and beginning graduate students interested in harmonic analysis.
650		0	_aHarmonic analysis _vTextbooks.
650		7	_aHarmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.).
650		7	_aHarmonic analysis on Euclidean spaces -- Research exposition (monographs, survey articles).
650		7	_aHarmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable.
650		7	_aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.
650		7	_aHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems.
700	1		_aWard, Lesley A.,
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-63-toc.pdf?_gl=1*15g3mh8*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTQ2NDk2MC41LjEuMTcxOTQ3OTczNS4wLjAuMA..
856			_3Index _uhttps://www.ams.org/bookstore/pspdf/stml-63-index.pdf?_gl=1*cldb7c*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTQ2NDk2MC41LjEuMTcxOTQ4MDM2Ni4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/14996999-harmonic-analysis?from_search=true&from_srp=true&qid=cpCYwOklj4&rank=1#CommunityReviews
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