Analysis on Fractals

By: Jun Kigami

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Paperback | 8 November 2010

At a Glance

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236 Pages

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22.86 x 15.24 x 1.37

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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.

Industry 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.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Topology Analytic Topology Medicine Medicine in General Probability & Statistics Calculus & Mathematical Analysis Differential Calculus & Equations

Other Editions and Formats

Hardcover

Published: 12th December 2001

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Introduction
Geometry of self-similar sets
Analysis on limits of networks
Construction of Laplacians on P. C. F. self-similar structures
Eigenvalues and eigenfunctions of Laplacians
Heat kernels
Additional fact
Mathematical backgrounds
Bibliography
List of notations
Index
Table of Contents provided by Publisher. All Rights Reserved.

Analysis on Fractals

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

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