# On Dirichlet-Schrödinger operators with strong potentials

Studia Mathematica (1995)

- Volume: 116, Issue: 3, page 239-254
- ISSN: 0039-3223

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topGrillo, Gabriele. "On Dirichlet-Schrödinger operators with strong potentials." Studia Mathematica 116.3 (1995): 239-254. <http://eudml.org/doc/216231>.

@article{Grillo1995,

abstract = {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.},

author = {Grillo, Gabriele},

journal = {Studia Mathematica},

keywords = {probabilistic methods; exponential decay at the boundary; Feynman-Kac functional},

language = {eng},

number = {3},

pages = {239-254},

title = {On Dirichlet-Schrödinger operators with strong potentials},

url = {http://eudml.org/doc/216231},

volume = {116},

year = {1995},

}

TY - JOUR

AU - Grillo, Gabriele

TI - On Dirichlet-Schrödinger operators with strong potentials

JO - Studia Mathematica

PY - 1995

VL - 116

IS - 3

SP - 239

EP - 254

AB - 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.

LA - eng

KW - probabilistic methods; exponential decay at the boundary; Feynman-Kac functional

UR - http://eudml.org/doc/216231

ER -

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