Geodesic
On Dirichlet-Schrödinger operators with strong potentials
Studia Mathematica, Tome 116 (1995) no. 3, pp. 239-254

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider Schrödinger operators H = -Δ/2 + V (V≥0 and locally bounded) with Dirichlet boundary conditions, on any open and connected subdomain $D ⊂ ℝ^n$ which either is bounded or satisfies the condition $d(x,D^{c}) → 0$ as |x| → ∞. We prove exponential decay at the boundary of all the eigenfunctions of H whenever V diverges sufficiently fast at the boundary ∂D, in the sense that $d(x,D^C)^{2}V(x) → ∞$ as $d(x,D^C) → 0$. We also prove bounds from above and below for Tr(exp[-tH]), and in particular we give criterions for the finiteness of such trace. Applications to pointwise bounds for the integral kernel of exp[-tH] and to the computation of expected values of the Feynman-Kac functional with respect to Doob h-conditioned measures are given as well.
DOI : 10.4064/sm-116-3-239-254

Gabriele Grillo 1

1 
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Gabriele Grillo. On Dirichlet-Schrödinger operators with strong potentials. Studia Mathematica, Tome 116 (1995) no. 3, pp. 239-254. doi: 10.4064/sm-116-3-239-254

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