Estimates of global bounds for some Schrödinger heat kernels on manifolds
Zhang, Qi S. ; Zhao, Z.
Illinois J. Math., Tome 44 (2000) no. 4, p. 556-573 / Harvested from Project Euclid
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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].
Publié le : 2000-09-15
Classification:  58J35,  35B45,  35K05 
@article{1256060416,
     author = {Zhang, Qi S. and Zhao, Z.},
     title = {Estimates of global bounds for some Schr\"odinger heat kernels on manifolds},
     journal = {Illinois J. Math.},
     volume = {44},
     number = {4},
     year = {2000},
     pages = { 556-573},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256060416}
}

Zhang, Qi S.; Zhao, Z. Estimates of global bounds for some Schrödinger heat kernels on manifolds. Illinois J. Math., Tome 44 (2000) no. 4, pp.  556-573. http://gdmltest.u-ga.fr/item/1256060416/