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Proceedings of the American Mathematical Society Series B

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Zero energy scattering for one-dimensional Schrödinger operators and applications to dispersive estimates


Authors: Iryna Egorova, Markus Holzleitner and Gerald Teschl
Journal: Proc. Amer. Math. Soc. Ser. B 2 (2015), 51-59
MSC (2010): Primary 34L25, 35Q41; Secondary 81U30, 81Q15
DOI: https://doi.org/10.1090/bproc/19
Published electronically: December 7, 2015
MathSciNet review: 3450570
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Abstract: We show that for a one-dimensional Schrödinger operator with a potential, whose $ (j+1)$-th moment is integrable, the $ j$-th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.


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Additional Information

Iryna Egorova
Affiliation: B. Verkin Institute for Low Temperature Physics, 47, Lenin ave, 61103 Kharkiv, Ukraine
Email: iraegorova@gmail.com

Markus Holzleitner
Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Email: amhang1@gmx.at

Gerald Teschl
Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria — and — International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
Email: Gerald.Teschl@univie.ac.at

DOI: https://doi.org/10.1090/bproc/19
Keywords: Schr\"odinger equation, scattering, resonant case, dispersive estimates
Received by editor(s): April 22, 2015
Received by editor(s) in revised form: August 17, 2015
Published electronically: December 7, 2015
Additional Notes: This research was supported by the Austrian Science Fund (FWF) under Grants No. Y330 and W1245
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)

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