Transport in the onedimensional Schrödinger equation
Author:
Michael Goldberg
Journal:
Proc. Amer. Math. Soc. 135 (2007), 31713179
MSC (2000):
Primary 35Q40; Secondary 34L25
Published electronically:
May 10, 2007
MathSciNet review:
2322747
Fulltext PDF Free Access
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Abstract: We prove a dispersive estimate for the Schrödinger equation on the real line, mapping between weighted spaces with stronger timedecay ( versus ) than is possible on unweighted spaces. To satisfy this bound, the longterm behavior of solutions must include transport away from the origin. Our primary requirements are that be integrable and not have a resonance at zero energy. If a resonance is present (for example, in the free case), similar estimates are valid after projecting away from a rankone subspace corresponding to the resonance.
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Additional Information
Michael Goldberg
Affiliation:
Department of Mathematics, Johns Hopkins University, 3400 N. Charles St., Baltimore, Maryland 21218
Email:
mikeg@math.jhu.edu
DOI:
http://dx.doi.org/10.1090/S0002993907088971
PII:
S 00029939(07)088971
Keywords:
Schr\"odinger equation,
dispersive estimates,
transport,
Jost solutions,
scattering theory
Received by editor(s):
June 12, 2006
Published electronically:
May 10, 2007
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
