Softcover ISBN:  9781470471996 
Product Code:  STML/105 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470474324 
Product Code:  STML/105.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470471996 
eBook: ISBN:  9781470474324 
Product Code:  STML/105.B 
List Price:  $118.00 $88.50 
Softcover ISBN:  9781470471996 
Product Code:  STML/105 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470474324 
Product Code:  STML/105.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470471996 
eBook ISBN:  9781470474324 
Product Code:  STML/105.B 
List Price:  $118.00 $88.50 

Book DetailsStudent Mathematical LibraryIAS/Park City Mathematics SubseriesVolume: 105; 2023; 279 ppMSC: Primary 31; 42; 28
This book gives a selfcontained introduction to the modern ideas and problems of harmonic analysis. Intended for third and fourthyear 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 indepth 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 selfstudy.
ReadershipUndergraduate and graduate students interested in Fourier analysis and harmonic analysis.

Table of Contents

Chapters

Motivation and preliminaries

Basic properties

Fourier series

Poisson kernel in the halfspace

Measure theory in Euclidean space

Lebesgue integral and Lebesgue spaces

Maximal functions

Fourier transform

Hilbert transform

Mathematics of fractals

The Laplacian on the Sierpiński gasket

Eigenfunctions of the Laplacian

Harmonic functions on postcritically finite sets

Some results from real analysis


Additional Material

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
This book gives a selfcontained introduction to the modern ideas and problems of harmonic analysis. Intended for third and fourthyear 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 indepth 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 selfstudy.
Undergraduate and graduate students interested in Fourier analysis and harmonic analysis.

Chapters

Motivation and preliminaries

Basic properties

Fourier series

Poisson kernel in the halfspace

Measure theory in Euclidean space

Lebesgue integral and Lebesgue spaces

Maximal functions

Fourier transform

Hilbert transform

Mathematics of fractals

The Laplacian on the Sierpiński gasket

Eigenfunctions of the Laplacian

Harmonic functions on postcritically finite sets

Some results from real analysis