A Singular Critical Potential For The Schrodinger operator

Details A Singular Critical Potential For The Schrodinger operator A Singular Critical Potential For The Schrodinger operator

2003-10-20

arxiv.org/abs/math/0310309v1

Mathematics

Analysis of PDEs

Scientific paper

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

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