Intrinsic ultracontractivity for Schrodinger operators based on fractional Laplacians
| dc.creator | Kaleta, Kamil | |
| dc.creator | Kulczycki, Tadeusz | |
| dc.date | 2009-04-28 | |
| dc.date.accessioned | 2026-07-07T13:09:25Z | |
| dc.date.available | 2026-07-07T13:09:25Z | |
| dc.description | We study the Feynman-Kac semigroup generated by the Schr{ö}dinger operator based on the fractional Laplacian $-(-Δ)^{α/2} - q$ in $\Rd$, for $q \ge 0$, $α\in (0,2)$. We obtain sharp estimates of the first eigenfunction $ϕ_1$ of the Schr{ö}dinger operator and conditions equivalent to intrinsic ultracontractivity of the Feynman-Kac semigroup. For potentials $q$ such that $\lim_{|x| \to \infty} q(x) = \infty$ and comparable on unit balls we obtain that $ϕ_1(x)$ is comparable to $(|x| + 1)^{-d - α} (q(x) + 1)^{-1}$ and intrinsic ultracontractivity holds iff $\lim_{|x| \to \infty} q(x)/\log|x| = \infty$. Proofs are based on uniform estimates of $q$-harmonic functions. | |
| dc.identifier | https://arxiv.org/abs/0904.4386 | |
| dc.identifier | http://arxiv.org/abs/0904.4386 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228726 | |
| dc.subject | Probability | |
| dc.subject | Spectral Theory | |
| dc.subject | 47G30, 60G52 | |
| dc.title | Intrinsic ultracontractivity for Schrodinger operators based on fractional Laplacians | |
| dc.type | text |