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A Limiting Absorption Principle for the Three-Dimensional Schrödinger Equation with L^p Potentials

Goldberger, M. and Schlag, W. (2004) A Limiting Absorption Principle for the Three-Dimensional Schrödinger Equation with L^p Potentials. International Mathematics Research Notices, 2004 (75). pp. 4049-4071. ISSN 1073-7928. doi:10.1155/S1073792804140324.

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We obtain mapping estimates for the Schrödinger resolvent (-Δ + V - λ^2)^(-1) in R^3, where the potential is assumed to satisfy only an integrability condition. No pointwise decay or additional regularity is required. These results are closely related to Agmon's limiting absorption principle, and also to the Stein-Tomas theorem in Fourier analysis.

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Additional Information:© 2004 Hindawi Publishing Corporation. Received January 27, 2004. Revision received August 24, 2004. Accepted October 28, 2004. The second author was supported by the NSF Grant DMS-0300081 and a Sloan fellowship.The authors wish to thank the referee for numerous suggestions.
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Sloan FellowshipUNSPECIFIED
Issue or Number:75
Record Number:CaltechAUTHORS:20111013-075612442
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Official Citation:M. Goldberg and W. Schlag A limiting absorption principle for the three-dimensional Schrödinger equation with Lp potentials Int Math Res Notices (2004) Vol. 2004 4049-4071 doi:10.1155/S1073792804140324
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27205
Deposited By: Ruth Sustaita
Deposited On:13 Oct 2011 15:57
Last Modified:09 Nov 2021 16:46

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