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Dispersive Estimates for Schrödinger Operators in Dimensions One and Three

Goldberg, Michael and Schlag, Wilhelm (2004) Dispersive Estimates for Schrödinger Operators in Dimensions One and Three. Communications in Mathematical Physics, 251 (1). pp. 157-178. ISSN 0010-3616. doi:10.1007/s00220-004-1140-5.

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We consider L^1→L^∞ estimates for the time evolution of Hamiltonians H=−Δ+V in dimensions d=1 and d=3 with bound t^(-∂/2). We require decay of the potentials but no regularity. In d=1 the decay assumption is ∫(1+|x|)|V(x)|dx<∞, whereas in d=3 it is |V(x)|≤C(1+|x|)^(−3−).

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Additional Information:© 2004 Springer-Verlag. Received: 5 June 2003 / Accepted: 5 January 2004 / Published online: 27 August 2004. Supported by the NSF grant DMS-0070538 and a Sloan fellowship. Communicated by B. Simon.
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Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20170408-133838992
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Official Citation:Goldberg, M. & Schlag, W. Commun. Math. Phys. (2004) 251: 157. doi:10.1007/s00220-004-1140-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75873
Deposited By: 1Science Import
Deposited On:13 Apr 2017 20:21
Last Modified:15 Nov 2021 16:55

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