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Fractal geometry and dynamical systems in pure and applied mathematics I : fractals in pure mathematics /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2013.
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| Colección: | Contemporary mathematics (American Mathematical Society) ;
Volume 600. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Separation Conditions for Iterated Function Systems with Overlaps; 1. Introduction; 2. Preliminaries; 3. The finite type condition; 4. More on the finite type condition; 5. Generalized finite type condition; 6. Weak separation condition; References; -point Configurations of Discrete Self-Similar Sets; 1. Introduction; 2. Lower bounds for -point configurations of compatible fractals; 3. Determinant fractal zeta functions; References; Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator; 1. Introduction.
- 4.2. Fractal strings and the (modified) Weyl-Berry conjecture.5. Quasi-Invertibility and Almost Invertibility of the Spectral Operator; 5.1. The truncated operators {̂( )}_{ } and {̂( )}_{ }.; 5.2. The spectra of _{ }{̂( )} and {̂( )}_{ }.; 5.3. Quasi-invertibility of _{ }, almost invertibility and Riemann zeroes.; 6. Spectral Reformulations of the Riemann Hypothesis and of Almost RH; 6.1. Quasi-invertibility of _{ } and spectral reformulation of RH; 6.2. Almost invertibility of _{ } and spectral reformulation of "Almost RH".
- 6.3. Invertibility of the spectral operator and phase transitions.7. Concluding Comments; 7.1. Extension to arithmetic zeta functions.; 7.2. Operator-valued Euler products.; 7.3. Global spectral operator.; 7.4. Towards a quantization of number theory.; 8. Appendix A:Riemann's Explicit Formula; 9. Appendix B:The Momentum Operator and Normality of _{ }; References; Analysis and Geometry of the Measurable Riemannian Structure on the Sierpiński Gasket; 1. Introduction; 2. Sierpiński gasket and its standard Dirichlet form; 3. Measurable Riemannian structure on the Sierpiński gasket.
- 4. Geometry under the measurable Riemannian structure5. Short time asymptotics of the heat kernels; 5.1. Intricsic metrics and off-diagonal Gaussian behavior; 5.2. One-dimensional asymptotics at vertices; 5.3. On-diagonal asymptotics at almost every point; 6. Ahlfors regularity and singularity of Hausdorff measure; 7. Weyl's Laplacian eigenvalue asymptotics; 8. Connections to general theories on metric measure spaces; 8.1. Identification of Dirichlet form as Cheeger energy; 8.2. Invalidity of Ricci curvature lower bound; 9. Possible generalizations to other self-similar fractals.