## Illinois Journal of Mathematics

### Estimates of global bounds for some Schrödinger heat kernels on manifolds

#### Abstract

We establish global bounds for the heat kernel of Schrödinger operators $-\Delta + V$ where $V$ is a certain long range potential. As a consequence we find some conditions for the heat kernel to have global Gaussian lower and upper bound. Some of the conditions are sharp if the potential does not change sign. We also provide a generalized Liouville theorem for Schrödinger operators and a refined version of the trace formula of Sa Barreto and Zworski [SZ].

#### Article information

Source
Illinois J. Math., Volume 44, Issue 3 (2000), 556-573.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256060416

Digital Object Identifier
doi:10.1215/ijm/1256060416

Mathematical Reviews number (MathSciNet)
MR1772429

Zentralblatt MATH identifier
0985.35016

Subjects
Primary: 58J35: Heat and other parabolic equation methods
Secondary: 35B45: A priori estimates 35K05: Heat equation

#### Citation

Zhang, Qi S.; Zhao, Z. Estimates of global bounds for some Schrödinger heat kernels on manifolds. Illinois J. Math. 44 (2000), no. 3, 556--573. doi:10.1215/ijm/1256060416. https://projecteuclid.org/euclid.ijm/1256060416