A Singular Critical Potential For The Schrodinger operator

Thomas Duyckaerts

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A Singular Critical Potential For The Schrodinger operator

Thomas Duyckaerts

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Abstract

We construct a potential $V$ on $\RR^d$, smooth away from one pole, and a sequence of quasi-modes for the operator $-Δ+V$, which concentrate on this pole. No smoothing effect, Strichartz estimates nor dispersive inequalities hold for the corresponding Schrodinger equation.

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Thomas Duyckaerts. 2003-10-20. A Singular Critical Potential For The Schrodinger operator. https://arxiv.org/abs/math/0310309

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