Analysis on Fractals

By: Jun Kigami, Bela Bollobas (Editor), W. Fulton (Editor)

Write A Review

Hardcover | 12 December 2001

At a Glance

Hardcover
236 Pages

Dimensions(cm)
22.86 x 15.24 x 1.75

Hardcover

RRP $214.95

$179.25

17%OFF

or 4 interest-free payments of $44.81 with

or

Aims to ship in 7 to 10 business days

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.

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.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Topology

Advanced Calculus (Revised Edition)

Paperback

RRP $54.99

$48.25

12%
OFF

Handbook of Geometry and Topology of Singularities VII - José Luis Cisneros-Molina

$64.50

Low Dimensional Topology and Number Theory : Fukuoka, Japan, March 15-18, 2022. In Memory of Professor Toshie Takata - Masanori Morishita

$39.75

36%
OFF

The Four Corners of Mathematics

A Brief History, from Pythagoras to Perelman

Hardcover

RRP $252.00

$178.40

29%
OFF

$222.90

29%
OFF

Twisted Morse Complexes : Morse Homology and Cohomology with Local Coefficients - Augustin Banyaga

$178.40

29%
OFF

Sheaf Theory through Examples

A User's Guide

Paperback

$103.35

Introduction	p. 1
Geometry of Self-Similar Sets	p. 8
Construction of self-similar sets	p. 8
Shift space and self-similar sets	p. 12
Self-similar structure	p. 17
Self-similar measure	p. 25
Dimension of self-similar sets	p. 28
Connectivity of self-similar sets	p. 33
Analysis on Limits of Networks	p. 41
Dirichlet forms and Laplacians on a finite set	p. 41
Sequence of discrete Laplacians	p. 51
Resistance from and resistance metric	p. 55
Dirichlet forms and Laplacians on limits of networks	p. 63
Construction of Laplacians on P. C. F. Self-Similar Structures	p. 68
Harmonic structures	p. 69
Harmonic functions	p. 73
Topology given by effective resistance	p. 83
Dirichlet forms on p. c. f. self-similar sets	p. 88
Green's function	p. 94
Green's operator	p. 102
Laplacians	p. 107
Nested fractals	p. 115
Eigenvalues and Eigenfunctions of Laplacians	p. 131
Eigenvalues and eigenfunctions	p. 132
Relation between dimensions	p. 137
Localized eigenfunctions	p. 141
Existence of localized eigenfunctions	p. 146
Estimate of eigenfunctions	p. 152
Heat Kernels	p. 157
Construction of heat kernels	p. 158
Parabolic maximum principle	p. 164
Asymptotic behavior of the heat kernels	p. 171
Additional Facts	p. 180
Mathematical Background	p. 196
Bibliography	p. 212
Index of Notation	p. 221
Index	p. 222
Table of Contents provided by Blackwell. All Rights Reserved.

Analysis on Fractals

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Topology

Advanced Calculus (Revised Edition)

Handbook of Geometry and Topology of Singularities VII

Braids, Conformal Module, Entropy, and Gromov's Oka Principle

Lecture Notes in Mathematics

Four Open Questions for the N-Body Problem

Low Dimensional Topology and Number Theory

Fukuoka, Japan, March 15-18, 2022. In Memory of Professor Toshie Takata

An Introduction to Module Theory

Oxford Graduate Texts in Mathematics

An Introduction to Module Theory

Oxford Graduate Texts in Mathematics

Symmetry in Geometry and Analysis, Volume 2

Festschrift in Honor of Toshiyuki Kobayashi

Symmetry in Geometry and Analysis, Volume 3

Festschrift in Honor of Toshiyuki Kobayashi

tale Cohomology

Category Theory Using Haskell

An Introduction with Moggi and Yoneda

Mathematical Analysis

Theory and Applications

Introduction to Topology 2nd Edition

Second Edition

SOLVING PROB IN GEOMETRY (V10)

Insights and Strategies for Mathematical Olympiad and Competitions

The Four Corners of Mathematics

A Brief History, from Pythagoras to Perelman

The Four Corners of Mathematics

A Brief History, from Pythagoras to Perelman

Graph Vision

Digital Architecture's Skeletons

COMBINATORIAL KNOT THEORY

Series on Knots & Everything

Handbook of Homotopy Theory

CRC Press/Chapman and Hall Handbooks in Mathematics

Twisted Morse Complexes

Morse Homology and Cohomology with Local Coefficients

SOLVING PROBLEMS IN POINT GEOMETRY

Insights and Strategies for Mathematical Olympiad and Competitions

SOLVING PROBLEMS IN POINT GEOMETRY

Insights and Strategies for Mathematical Olympiad and Competitions

Advances in Algebra Analysis and Topology

Sheaf Theory through Examples

A User's Guide

This product is categorised by