000			02865nam a22003377a 4500
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005			20240625153109.0
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020			_a9781470471996
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a517.57 _bSAE-I
100			_aSáenz, Ricardo A.
245			_aIntroduction to harmonic analysis
260			_aRhode Island : _bAmerican Mathematical Society, _c2023.
300			_axv, 279p.
490			_aStudent mathematical library, IAS/Park City mathematical subseries _vvolume 105. _x1520-9121 ;
504			_aIncludes bibliographical references and index.
520			_aThis book gives a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure theory, Lebesgue integration and approximation theorems. The book motivates the study of harmonic functions by describing the Dirichlet problem, and discussing examples such as solutions to the heat equation in equilibrium, the real and imaginary parts of holomorphic functions, and the minimizing functions of energy. It then leads students through an in-depth study of the boundary behavior of harmonic functions and finishes by developing the theory of harmonic functions defined on fractals domains. The book is designed as a textbook for an introductory course on classical harmonic analysis, or for a course on analysis on fractals. Each chapter contains exercises, and bibliographic and historical notes. The book can also be used as a supplemental text or for self-study.
521			_aUndergraduate and graduate students interested in Fourier analysis and harmonic analysis.
650		0	_aHarmonic analysis.
650		7	_aPotential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions.
650		7	_aPotential theory -- Higher-dimensional theory -- Integral representations, integral operators, integral equations methods.
650		7	_aPotential theory -- Higher-dimensional theory -- Boundary behavior.
650		7	_aHarmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series.
650		7	_aMaximal functions, Littlewood-Paley theory.
650		7	_aMeasure and integration -- Classical measure theory -- Fractals.
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-105-toc.pdf?_gl=1*ixgi0q*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMwODk2NS4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/195951043-introduction-to-harmonic-analysis?ref=nav_sb_ss_1_13#CommunityReviews
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