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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View in AMS MathViewer

Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
213624

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

MR Author ID:
360802

Email:
Gerald.Teschl@univie.ac.at

Keywords:
Schrödinger 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 authors under
Creative Commons Attribution 3.0 License
(CC BY 3.0)