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- W2952266936 abstract "We study the Feynman-Kac semigroup generated by the Schr{o}dinger operator based on the fractional Laplacian $-(-Delta)^{alpha/2} - q$ in $Rd$, for $q ge 0$, $alpha in (0,2)$. We obtain sharp estimates of the first eigenfunction $phi_1$ of the Schr{o}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 $phi_1(x)$ is comparable to $(|x| + 1)^{-d - alpha} (q(x) + 1)^{-1}$ and intrinsic ultracontractivity holds iff $lim_{|x| to infty} q(x)/log|x| = infty$. Proofs are based on uniform estimates of $q$-harmonic functions." @default.
- W2952266936 created "2019-06-27" @default.
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- W2952266936 date "2009-04-28" @default.
- W2952266936 modified "2023-09-27" @default.
- W2952266936 title "Intrinsic ultracontractivity for Schrodinger operators based on fractional Laplacians" @default.
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