A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

M. Burak Erdoǧan; William R. Green

doi:10.1007/s00220-012-1640-7

A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

M. Burak Erdoǧan, William R. Green

Mathematics

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

Abstract

Let H = -Δ + V, where V is a real valued potential on ℝ² satisfying {pipe}V(x){pipe}≲〈 x 〉^-3-. We prove that if zero is a regular point of the spectrum of H = -Δ + V, then, with w(x) = (log(2 + {pipe}x{pipe}))². This decay rate was obtained by Murata in the setting of weighted L² spaces with polynomially growing weights.

Original language	English (US)
Pages (from-to)	791-811
Number of pages	21
Journal	Communications in Mathematical Physics
Volume	319
Issue number	3
DOIs	https://doi.org/10.1007/s00220-012-1640-7
State	Published - May 2013

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-012-1640-7

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abstract = "Let H = -Δ + V, where V is a real valued potential on ℝ2 satisfying {pipe}V(x){pipe}≲〈 x 〉-3-. We prove that if zero is a regular point of the spectrum of H = -Δ + V, then, with w(x) = (log(2 + {pipe}x{pipe}))2. This decay rate was obtained by Murata in the setting of weighted L2 spaces with polynomially growing weights.",

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N2 - Let H = -Δ + V, where V is a real valued potential on ℝ2 satisfying {pipe}V(x){pipe}≲〈 x 〉-3-. We prove that if zero is a regular point of the spectrum of H = -Δ + V, then, with w(x) = (log(2 + {pipe}x{pipe}))2. This decay rate was obtained by Murata in the setting of weighted L2 spaces with polynomially growing weights.

AB - Let H = -Δ + V, where V is a real valued potential on ℝ2 satisfying {pipe}V(x){pipe}≲〈 x 〉-3-. We prove that if zero is a regular point of the spectrum of H = -Δ + V, then, with w(x) = (log(2 + {pipe}x{pipe}))2. This decay rate was obtained by Murata in the setting of weighted L2 spaces with polynomially growing weights.

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A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

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