ENGLISH

Introduction to Harmonic Analysis (Student Mathematical Library)

By Ricardo A. Sáenz

Book information

Publisher
American Mathematical Society
Year
1996
ISBN
147047199X, 9781470471996
Language
english
Format
PDF
Filesize
4 MB (4118195 bytes)
Pages
279\296
Time added
2023-10-19 04:39:00

Description

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.

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