Analysis on Fractals

Jun Kigami (Kyoto University, Japan), B. Bollobas, W. Fulton , A. Katok

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English

Cambridge University Press
12 December 2001

Calculus & mathematical analysis; Geometry; Analytic topology

Series: Cambridge Tracts in Mathematics

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.

By: Jun Kigami (Kyoto University Japan)
Series edited by: B. Bollobas, W. Fulton, A. Katok, F. Kirwan
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 143
Dimensions: Height: 237mm, Width: 159mm, Spine: 20mm
Weight: 460g
ISBN: 9780521793216
ISBN 10: 0521793211
Series: Cambridge Tracts in Mathematics
Pages: 236
Publication Date: 12 December 2001
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Analysis on Fractals

'... 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.