Analysis on Fractals (Cambridge Tracts in Mathematics) [Hardcover]

Jun Kigami (Author)

Book Description

ISBN-10: 0521793211 | ISBN-13: 978-0521793216 | Publication Date: June 11, 2001

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.

Editorial Reviews

Review

'... 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.

Book Description

This book covers analysis on fractals, a developing area of mathematics focusing on the dynamical aspects of fractals. It provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and then goes on to discuss recent results. 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, in mathematics and physics departments.

Product Details

• Hardcover: 236 pages
• Publisher: Cambridge University Press (June 11, 2001)
• Language: English
• ISBN-10: 0521793211
• ISBN-13: 978-0521793216
• Product Dimensions: 6 x 9 x 0.7 inches
• Shipping Weight: 8.5 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #4,269,324 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful:

5.0 out of 5 stars Metrics, fractals, analysis..., February 24, 2003

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This review is from: Analysis on Fractals (Cambridge Tracts in Mathematics) (Hardcover)

Fractals make headlines from time to time[--are they everywhere?], and and they make beautiful color pictures; but they are also part of a substantial mathematical theory, even one with an exciting mathematical history. This lovely book presents the subject elegantly in a way that it can be taught to students. It starts with the basics, then systematically, step by step, it builds up the central results. Great for the classrom, or for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. Example: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. Compared to other books at the same level, for example, by Falconer, 1990, and the equally attractive one from 1985[Falconer: The geometry of fractal sets], Kigami's book stresses the analysis of the Laplace operator. Falconer covers the theory more generally, and his books have a slightly more potential theoretic bent.