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• W2024282433 endingPage "1248" @default.
• W2024282433 startingPage "1215" @default.
• W2024282433 abstract "We study Schrödinger semigroups in the scale of Sobolev spaces, and show that, for Kato class potentials, the range of such semigroups in Lp has exactly two more derivatives than the potential; this proves a conjecture of B. Simon. We show that eigenfunctions of Schrödinger operators are generically smoother by exactly two derivatives (in given Sobolev spaces) than their potentials. We give applications to the relation between the potential's smoothness and particle kinetic energy in the context of quantum mechanics, and characterize kinetic energies in Coulomb systems. The techniques of proof involve Leibniz and chain rules for fractional derivatives which are of independent interest, as well as a new characterization of the Kato class." @default.
• W2024282433 created "2016-06-24" @default.
• W2024282433 creator A5067228319 @default.
• W2024282433 creator A5070448763 @default.
• W2024282433 date "1996-01-01" @default.
• W2024282433 modified "2023-10-18" @default.
• W2024282433 title "Exact smoothing properties of Schrodinger semigroups" @default.
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• W2024282433 doi "https://doi.org/10.1353/ajm.1996.0050" @default.
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