Analysis on fractals /
Saved in:
| Author / Creator: | Kigami, Jun. |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2001. |
| Description: | 226 p. : ill. ; 23 cm. |
| Language: | English |
| Series: | Cambridge tracts in mathematics. 143 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4488797 |
Table of Contents:
- 1. Geometry of Self-Similar Sets
- 1.1. Construction of self-similar sets
- 1.2. Shift space and self-similar sets
- 1.3. Self-similar structure
- 1.4. Self-similar measure
- 1.5. Dimension of self-similar sets
- 1.6. Connectivity of self-similar sets
- 2. Analysis on Limits of Networks
- 2.1. Dirichlet forms and Laplacians on a finite set
- 2.2. Sequence of discrete Laplacians
- 2.3. Resistance from and resistance metric
- 2.4. Dirichlet forms and Laplacians on limits of networks
- 3. Construction of Laplacians on P. C. F. Self-Similar Structures
- 3.1. Harmonic structures
- 3.2. Harmonic functions
- 3.3. Topology given by effective resistance
- 3.4. Dirichlet forms on p. c. f. self-similar sets
- 3.5. Green's function
- 3.6. Green's operator
- 3.7. Laplacians
- 3.8. Nested fractals
- 4. Eigenvalues and Eigenfunctions of Laplacians
- 4.1. Eigenvalues and eigenfunctions
- 4.2. Relation between dimensions
- 4.3. Localized eigenfunctions
- 4.4. Existence of localized eigenfunctions
- 4.5. Estimate of eigenfunctions
- 5. Heat Kernels
- 5.1. Construction of heat kernels
- 5.2. Parabolic maximum principle
- 5.3. Asymptotic behavior of the heat kernels. App. A. Additional Facts
- App. B. Mathematical Background.