Fractal analysis

Author: (Japanese) Kigami, J.
Publisher:
Publish Date: 2004-09-01
Features: This book discusses shape analysis, a rapidly developing branch of mathematics that primarily studies the dynamic properties of fractals, such as heat diffusion in fractals and the vibration of fractal structure materials. Starting from the geometric principles of basic self-similar sets, the book gradually discusses recent research findings, including the properties of eigenvalues and eigenfunctions of the Laplace operator, the asymptotic characteristics of heat kernels of self-similar sets, and more. Reading this book requires only a foundation in advanced analysis, general topology, and measure theory. It is particularly suitable for graduate students and researchers in analysis and probability theory. Additionally, it is an excellent introductory textbook for graduate-level courses on fractals and related topics.