A counterexample to dispersive estimates for Schrödinger operators in higher dimensions

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dc.creatorGoldberg, M.
dc.creatorVisan, M.
dc.date2005-08-11
dc.date.accessioned2026-07-07T06:31:24Z
dc.date.available2026-07-07T06:31:24Z
dc.descriptionIn dimension $n>3$ we show the existence of a compactly supported potential in the differentiability class $C^α$, $α< \frac{n-3}2$, for which the solutions to the linear Schrödinger equation in $\R^n$, $$ -i\partial_t u = - Δu + Vu, \quad u(0)=f, $$ do not obey the usual $L^1\to L^{\infty}$ dispersive estimate. This contrasts with known results in dimensions $n \leq 3$, where a pointwise decay condition on $V$ is generally sufficient to imply dispersive bounds.
dc.identifierhttps://arxiv.org/abs/math/0508206
dc.identifierhttp://arxiv.org/abs/math/0508206
dc.identifierComm. Math. Phys. 266 no. 1 (2006), 211-238.
dc.identifierdoi:10.1007/s00220-006-0013-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98591
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleA counterexample to dispersive estimates for Schrödinger operators in higher dimensions
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