Dispersive estimates for the Schrödinger equation for C n-3/2 potentials in odd dimensions

M. Burak Erdoǧan; William R. Green

doi:10.1093/imrn/rnp221

Dispersive estimates for the Schrödinger equation for C n-3/2 potentials in odd dimensions

M. Burak Erdoǧan
, William R. Green

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate L¹ → L^∞ dispersive estimates for the Schrödinger equation iut - δu+Vu=0 in odd dimensions greater than three. We obtain dispersive estimates under the optimal smoothness condition for the potential, V ∈ C ^(n-3)/2(ℝⁿ), in dimensions five and seven. We also describe a method to extend this result to arbitrary odd dimensions.

Original language	English (US)
Pages (from-to)	2532-2565
Number of pages	34
Journal	International Mathematics Research Notices
Volume	2010
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnp221
State	Published - Dec 2010

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General Mathematics

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10.1093/imrn/rnp221

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abstract = "We investigate L1 → L∞ dispersive estimates for the Schr{\"o}dinger equation iut - δu+Vu=0 in odd dimensions greater than three. We obtain dispersive estimates under the optimal smoothness condition for the potential, V ∈ C (n-3)/2(ℝn), in dimensions five and seven. We also describe a method to extend this result to arbitrary odd dimensions.",

author = "Erdoǧan, \{M. Burak\} and Green, \{William R.\}",

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N2 - We investigate L1 → L∞ dispersive estimates for the Schrödinger equation iut - δu+Vu=0 in odd dimensions greater than three. We obtain dispersive estimates under the optimal smoothness condition for the potential, V ∈ C (n-3)/2(ℝn), in dimensions five and seven. We also describe a method to extend this result to arbitrary odd dimensions.

AB - We investigate L1 → L∞ dispersive estimates for the Schrödinger equation iut - δu+Vu=0 in odd dimensions greater than three. We obtain dispersive estimates under the optimal smoothness condition for the potential, V ∈ C (n-3)/2(ℝn), in dimensions five and seven. We also describe a method to extend this result to arbitrary odd dimensions.

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Dispersive estimates for the Schrödinger equation for C n-3/2 potentials in odd dimensions

Abstract

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