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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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