Alonso-Ruiz, Patricia: Dirichlet forms on non self-similar sets : Hanoi attractors and the Sierpiński gasketDirichletformen auf nicht selbstähnlichen Mengen : Hanoi-Attraktoren und das Sierpinski-Dreieck. 2013
Inhalt
- Introduction
- Geometric approximation
- Analysis on the Sierpinski gasket K
- Analysis on the Hanoi attractor K
- Approximating forms
- Resistance and Dirichlet form on the Hanoi attractor K
- Laplacian on K
- A Borel regular measure on K
- Normal derivatives and Gauss-Green formula
- Green's function
- The spectrum of the Laplacian
- Spectral dimension
- Consequences and further research
- Appendix Theoretical background
- Bibliography