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15 February 2006 Agmon-Kato-Kuroda theorems for a large class of perturbations
Alexandru D. Ionescu, Wilhelm Schlag
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Duke Math. J. 131(3): 397-440 (15 February 2006). DOI: 10.1215/S0012-7094-06-13131-9

Abstract

We prove asymptotic completeness for operators of the form H=-Δ+L on L2(Rd), d2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials VLq(Rd), q[d/2,(d+1)/2] (if d=2, then we require q(1,3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible perturbations also contains first-order differential operators of the form a·-·a̲ for suitable vector potentials a. Our main technical statement is a new limiting absorption principle, which we prove using techniques from harmonic analysis related to the Stein-Tomas restriction theorem

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Alexandru D. Ionescu. Wilhelm Schlag. "Agmon-Kato-Kuroda theorems for a large class of perturbations." Duke Math. J. 131 (3) 397 - 440, 15 February 2006. https://doi.org/10.1215/S0012-7094-06-13131-9

Information

Published: 15 February 2006
First available in Project Euclid: 6 February 2006

zbMATH: 1092.35073
MathSciNet: MR2219246
Digital Object Identifier: 10.1215/S0012-7094-06-13131-9

Subjects:
Primary: 47A10
Secondary: 35P05

Rights: Copyright © 2006 Duke University Press

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Vol.131 • No. 3 • 15 February 2006
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