Continuity properties of integral kernels associated with Schroedinger operators on manifolds

Bruening, Jochen; Geyler, Vladimir; Pankrashkin, Konstantin

Continuity properties of integral kernels associated with Schroedinger operators on manifolds

Authors

Bruening, Jochen

Geyler, Vladimir

Pankrashkin, Konstantin

Description

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)