Continuity properties of integral kernels associated with Schroedinger operators on manifolds

Abstract

For Schroedinger operators (including those with magnetic fields) with singular (locally integrable) scalar potentials on manifolds of bounded geometry, we study continuity properties of some related integral kernels: the heat kernel, the Green function, and also kernels of some other functions of the operator. In particular, we show the joint continuity of the heat kernel and the continuity of the Green function outside the diagonal. The proof makes intensive use of the Lippmann-Schwinger equation.

38 pages, major revision; to appear in Annales Henri Poincare (2007)

References in corpus (4)

• Essential self-adjointness of Schroedinger type operators on manifolds
• Heat Kernel Approach in Quantum Field Theory
• Continuous integral kernels for unbounded Schroedinger semigroups and their spectral projections
• On-diagonal singularities of the Green functions for Schroedinger operators

Cited by in corpus (4)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• On-diagonal singularities of the Green functions for Schroedinger operators
• A rigorous approach to the magnetic response in disordered systems
• Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields