Introduction to Harmonic Analysis
Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-7199-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7199-6 (ISBN)
Provides 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.
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.
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.
Ricardo A. Saenz, Universidad de Colima, Mexico.
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 Sierpinski gasket
Eigenfunctions of the Laplacian
Harmonic functions on post-critically finite sets
Some results from real analysis
Bibliography
Index.
| Erscheinungsdatum | 24.08.2023 |
|---|---|
| Reihe/Serie | Student Mathematical Library |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 140 x 216 mm |
| Gewicht | 174 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-7199-X / 147047199X |
| ISBN-13 | 978-1-4704-7199-6 / 9781470471996 |
| Zustand | Neuware |
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