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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the decay properties of solutions to a class of Schrödinger equations


Authors: L. Dawson, H. McGahagan and G. Ponce
Journal: Proc. Amer. Math. Soc. 136 (2008), 2081-2090
MSC (2000): Primary 35J10; Secondary 35B65
Published electronically: February 14, 2008
MathSciNet review: 2383514
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Abstract: We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrödinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections $ P_\pm$ onto the positive and negative frequencies.


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Additional Information

L. Dawson
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089
Email: ldawson@math.arizona.edu

H. McGahagan
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: helena@math.ucsb.edu

G. Ponce
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: ponce@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09355-6
PII: S 0002-9939(08)09355-6
Received by editor(s): March 6, 2007
Published electronically: February 14, 2008
Additional Notes: The first author was supported by NSF grants
The second author was supported by an NSF postdoctoral fellowship
The third author was supported by NSF grants
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2008 American Mathematical Society