Transport in the one-dimensional Schrödinger equation

Author:
Michael Goldberg

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3171-3179

MSC (2000):
Primary 35Q40; Secondary 34L25

Published electronically:
May 10, 2007

MathSciNet review:
2322747

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a dispersive estimate for the Schrödinger equation on the real line, mapping between weighted spaces with stronger time-decay ( versus ) than is possible on unweighted spaces. To satisfy this bound, the long-term 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 rank-one 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:
https://doi.org/10.1090/S0002-9939-07-08897-1

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.