English

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)