Analysis on Fractals

by Jun Kigami

Overview

This book covers analysis on fractals, a developing area of mathematics that 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.

Product Details

ISBN-13:	9780521057110
Publisher:	Cambridge University Press
Publication date:	03/01/2008
Series:	Cambridge Tracts in Mathematics , #143
Edition description:	New Edition
Pages:	236
Product dimensions:	5.98(w) x 9.02(h) x 0.55(d)

Table of Contents

Introduction; 1. Geometry of self-similar sets; 2. Analysis on limits of networks; 3. Construction of Laplacians on P. C. F. self-similar structures; 4. Eigenvalues and eigenfunctions of Laplacians; 5. Heat kernels; Appendix A: Additional fact; Appendix B: Mathematical backgrounds; Bibliography; List of notations; Index.

Editorial Reviews

'… the most recent introduction to the analysis of 'Laplacians' on what physicists call finitely ramified self-similar fractals.' Volker Metz, Zentralblatt MATH

'Anyone with a background in the analysis of linear field equations, with an interest in heterogeneous media, or who is looking to breathe new life into their research, should read this book.' A. J. Mulholland, Proceedings of the Edinburgh Mathematical Society

'This book is an introduction to the subject written by one of the active researchers in the area. It is recommended to those who would like to go from the basics to current research topics.' Acta. Sci. Math.

From the Publisher