Dispersive estimates for Schrödinger operators with measure-valued potentials in \(\mathbb R^3\) (Q2874073)
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scientific article; zbMATH DE number 6251197
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dispersive estimates for Schrödinger operators with measure-valued potentials in \(\mathbb R^3\) |
scientific article; zbMATH DE number 6251197 |
Statements
28 January 2014
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Schrödinger operators
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dispersive estimate
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resolvent
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Wiener algebra
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Fourier restriction
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Dispersive estimates for Schrödinger operators with measure-valued potentials in \(\mathbb R^3\) (English)
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In this paper, the author derives dispersive estimates for Schrödinger operators in 3 dimensions, the potential of which is a measure of large enough fractal dimension. The assumptions on the measure ensure that the potential is form-compact relative to the Laplacian and a short range perturbation. For the dispersive estimates, it is required that the Schrödinger operator has no positive eigenvalue and no zero resonance. This is natural in that context. Conditions on the measure are provided to meet this requirement. The proof is of perturbative nature and relies on a procedure already used in [\textit{M. Beceanu} and \textit{M. Goldberg}, Commun. Math. Phys. 314, No. 2, 471--481 (2012; Zbl 1250.35047)].
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