This book covers analysis on fractals, a developing area of
mathematics which focuses on the dynamical aspects of fractals,
such as heat diffusion on fractals and the vibration of a material
with fractal structure. The book provides a self-contained
introduction to the subject, starting from the basic geometry of
self-similar sets and going on to discuss recent results, including
the properties of eigenvalues and eigenfunctions of the Laplacians,
and the asymptotical behaviors of heat kernels on self-similar
sets. Requiring only a basic knowledge of advanced analysis,
general topology and measure theory, this book will be of value to
graduate students and researchers in analysis and probability
theory. It will also be useful as a supplementary text for graduate
courses covering fractals.
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