Continuity properties of integral kernels associated with Schroedinger operators on manifolds
Mathematical Physics
2007-12-18 v3 Functional Analysis
math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0410042,
title = {Continuity properties of integral kernels associated with Schroedinger operators on manifolds},
author = {Jochen Bruening and Vladimir Geyler and Konstantin Pankrashkin},
journal= {arXiv preprint arXiv:math-ph/0410042},
year = {2007}
}
Comments
38 pages, major revision; to appear in Annales Henri Poincare (2007)