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1995 | 116 | 3 | 239-254

Tytuł artykułu

On Dirichlet-Schrödinger operators with strong potentials

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Kategorie tematyczne

Czasopismo

Rocznik

Tom

116

Numer

3

Strony

239-254

Daty

wydano
1995
otrzymano
1994-12-13

Twórcy

  • Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy

Bibliografia

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