Softcover ISBN: | 978-1-4704-7199-6 |
Product Code: | STML/105 |
List Price: | $59.00 |
Individual Price: | $47.20 |
eBook ISBN: | 978-1-4704-7432-4 |
Product Code: | STML/105.E |
List Price: | $59.00 |
Individual Price: | $47.20 |
Softcover ISBN: | 978-1-4704-7199-6 |
eBook: ISBN: | 978-1-4704-7432-4 |
Product Code: | STML/105.B |
List Price: | $118.00 $88.50 |
Softcover ISBN: | 978-1-4704-7199-6 |
Product Code: | STML/105 |
List Price: | $59.00 |
Individual Price: | $47.20 |
eBook ISBN: | 978-1-4704-7432-4 |
Product Code: | STML/105.E |
List Price: | $59.00 |
Individual Price: | $47.20 |
Softcover ISBN: | 978-1-4704-7199-6 |
eBook ISBN: | 978-1-4704-7432-4 |
Product Code: | STML/105.B |
List Price: | $118.00 $88.50 |
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Book DetailsStudent Mathematical LibraryIAS/Park City Mathematics SubseriesVolume: 105; 2023; 279 ppMSC: Primary 31; 42; 28
This 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.
ReadershipUndergraduate and graduate students interested in Fourier analysis and harmonic analysis.
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Table of Contents
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Chapters
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Motivation and preliminaries
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Basic properties
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Fourier series
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Poisson kernel in the half-space
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Measure theory in Euclidean space
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Lebesgue integral and Lebesgue spaces
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Maximal functions
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Fourier transform
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Hilbert transform
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Mathematics of fractals
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The Laplacian on the Sierpiński gasket
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Eigenfunctions of the Laplacian
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Harmonic functions on post-critically finite sets
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Some results from real analysis
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Additional Material
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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 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.
Undergraduate and graduate students interested in Fourier analysis and harmonic analysis.
-
Chapters
-
Motivation and preliminaries
-
Basic properties
-
Fourier series
-
Poisson kernel in the half-space
-
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 post-critically finite sets
-
Some results from real analysis