Covariant Schrödinger semigroups on Riemannian manifolds

Abstract

This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specific results for the minimal heat kernel V. Wiener measure and Brownian motion on Riemannian manifolds VI. Contractive Dynkin and Kato potentials VII. Foundations of covariant Schrödinger semigroups VIII. Compactness of $V(H^{\nabla }+1{)}^{-1}$ IX. $L^q$-properties of covariant Schrödinger semigroups X. Continuity properties of covariant Schrödinger semigroups XI. Integral kernels for covariant Schrödinger semigroups XII. Essential self-adjointness of covariant Schrödinger semigroups XIII. Smooth compactly supported sections as form core XIV. Applications (in quantum mechanics and geometric analysis)

This is a shortened version (the Chapters VII - XIII have been removed). The full version has been published in December 2017 as a monograph in the BIRKHÄUSER series Operator Theory: Advances and Applications, and only the published version should be cited