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Dispersive Estimates for Schrödinger Operators in Dimension Two

Schlag, W. (2005) Dispersive Estimates for Schrödinger Operators in Dimension Two. Communications in Mathematical Physics, 257 (1). pp. 87-117. ISSN 0010-3616. doi:10.1007/s00220-004-1262-9.

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We prove L^1(ℝ^2)→L^∞(ℝ^2) for the two-dimensional Schrödinger operator −Δ+V with the decay rate t^(−1). We assume that zero energy is neither an eigenvalue nor a resonance. This condition is formulated as in the recent paper by Jensen and Nenciu on threshold expansions for the two-dimensional resolvent.

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Additional Information:© Springer-Verlag Berlin Heidelberg 2005. Received: 21 April 2004 / Accepted: 16 July 2004 / Published online: 11 January 2005. Communicated by B. Simon. The author was partially supported by the NSF grant DMS-0300081 and a Sloan Fellowship. The author wishes to thank Monica Visan for comments on a preliminary version of this paper, as well as the anonymous referee for a very careful reading and many helpful comments.
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Alfred P. Sloan FoundationUNSPECIFIED
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Record Number:CaltechAUTHORS:20170408-160721963
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Official Citation:Schlag, W. Commun. Math. Phys. (2005) 257: 87. doi:10.1007/s00220-004-1262-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76130
Deposited By: 1Science Import
Deposited On:21 Jun 2017 22:32
Last Modified:15 Nov 2021 16:57

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