Covariant Schroedinger Semigroups on Riemannian Manifolds

Sobolev spaces on vector bundles.- Smooth heat kernels on vector bundles.- Basis differential operators on Riemannian manifolds.- Some specific results for the minimal heat kernel.- Wiener measure and Brownian motion on Riemannian manifolds.- Contractive Dynkin potentials and Kato potentials.- Foundations of covariant Schroedinger semigroups.- Compactness of resolvents for covariant Schroedinger operators.- L^p properties of covariant Schroedinger semigroups.- Continuity properties of covariant Schroedinger semigroups.- Integral kernels for covariant Schroedinger semigroup.- Essential self-adjointness of covariant Schroedinger semigroups.- Form cores.- Applications.

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• Cálculo diferencial e equações
• Cálculo e análise matemática

covariant Schroedinger semigroup;heat semigroup;Schroedinger operators;Brownian motion on manifolds;spectral theory;partial differential equations