Analysis on Fractals
Analysis on Fractals
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.
- This is the first book on a new area of mathematics, analysis on fractals
- No special knowledge of fractals required
- Self contained: covers basic background material as well as recent research
Reviews & endorsements
'… 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.
Product details
February 2011Adobe eBook Reader
9780511836787
0 pages
0kg
12 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
