A Singular Critical Potential For The Schrodinger operator
classification
🧮 math.AP
keywords
operatorpolepotentialschrodingerawayconcentrateconstructcorresponding
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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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