Covariant Schrödinger Semigroups on Riemannian Manifolds

Develops basic vector-bundle-valued objects of geometric analysis from scratchGives a detailed proof of the Feynman-Kac fomula with singular potentials on manifolds
Includes previously unpublished results

Develops basic vector-bundle-valued objects of geometric analysis from scratch Gives a detailed proof of the Feynman-Kac fomula with singular potentials on manifolds Includes previously unpublished results

Inhalt
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 Schrödinger semigroups.- Compactness of resolvents for covariant Schrödinger operators.- L^p properties of covariant Schrödinger semigroups.- Continuity properties of covariant Schrödinger semigroups.- Integral kernels for covariant Schrödinger semigroup.- Essential self-adjointness of covariant Schrödinger semigroups.- Form cores.- Applications. <p