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Ubiquitous Heat Kernel.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2006.
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| Colección: | Contemporary Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Contents
- Preface
- Positivity of zeta distributions and small unitary representations
- The heat equation and representations of the Jacobi group
- Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians
- The heat kernel in low-dimensional quantum theories
- Heat kernels on weighted manifolds and applications
- 1. Introduction
- 2. The Laplace operator
- 2.1 Differential operators on manifolds
- 2.2 Laplacian as an operator in L2
- 2.3 Some examples
- 2.4 Laplacian on model manifolds
- 3. The heat kernel
- 3.1 Heat semigroup3.2 Heat kernel and fundamental solutions
- 3.3 Stochastic completeness
- 4. Relations between different heat kernels
- 4.1 Direct products
- 4.2 Isometries
- 4.3 Comparison of heat kernels
- 4.4 Change of measure
- 4.5 Some examples of heat kernels in R
- 4.6 Hyperbolic spaces
- 5. Heat kernel estimates
- 5.1 Uniform Faber-Krahn inequality
- 5.2 Gaussian upper bounds
- 5.3 On-diagonal lower bounds
- 5.4 Relative Faber-Krahn inequality
- 5.5 On-diagonal estimates on model manifolds
- ""5.6 Estimates with the mean curvature function""""5.7 Green function and Green operator""; ""6. Harnack inequality""; ""6.1 The Li-Yau estimate""; ""6.2 Manifolds with relatively connected annuli""; ""6.3 Non-uniform change of measure""; ""6.4 Conformal change of the metric tensor""; ""6.5 Manifolds with ends""; ""7. Eigenvalues of Schrödinger operators""; ""7.1 Negative eigenvalues""; ""7.2 Stability index of minimal surfaces""; ""8. The Brownian motion""; ""8.1 Construction of the Brownian motion""; ""8.2 The first exit time""; ""8.3 The Dirichlet problem for a Schrödinger operator""
- ""9. Path properties of stochastic processes""""9.1 Recurrence and transience""; ""9.2 Escape rate""; ""9.3 Recurrence and transience of Î"-process""; ""9.4 Asymptotic separation of trajectories of Î"-process""; ""10. Heat kernels of SchrÃœdinger operators""; ""10.1 Heat kernel and a ground state""; ""10.2 Green bounded potentials""; ""10.3 Potentials with a polynomial ground state""; ""10.4 Potentials of quadratic decay in Rn""; ""10.5 Spherically symmetric potentials""; ""10.6 Appendix: behavior of harmonic functions at â?ž""; ""References""
- ""Heat kernels in geometric evolution equations""""The range of the heat operator""; ""Heat kernels and cycles""; ""Green currents on KÃ?hler manifolds""; ""Heat kernels and Riesz transforms""; ""The contest between the kernels in the Selberg trace formula for the (q + 1)-regular tree""; ""Expressing Arakelov invariants using hyperbolic heat kernels""; ""Grassmanians of higher local fields and multivariable tau functions""; ""Heat kernels and the range of the trace on completions of twisted group algebras""; ""Theta functions, old and new""