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Mathematics > Spectral Theory

Title: Zero Energy Scattering for One-Dimensional Schrödinger Operators and Applications to Dispersive Estimates

Authors: Iryna Egorova, Markus Holzleitner, Gerald Teschl
(Submitted on 22 Apr 2015 (v1), last revised 8 Dec 2015 (this version, v2))
Abstract: We show that for a one-dimensional Schr\"odinger 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 Schr\"odinger equation in the resonant case.
Comments: 9 pages
Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: Primary 34L25, 35Q41, Secondary 81U30, 81Q15
Journal reference: Proc. Amer. Math. Soc. Ser. B 2, 51-59 (2015)
DOI: 10.1090/bproc/19
Cite as: arXiv:1504.05744 [math.SP]
  (or arXiv:1504.05744v2 [math.SP] for this version)

Submission history

From: Gerald Teschl [view email]
[v1] Wed, 22 Apr 2015 11:41:11 GMT (10kb)
[v2] Tue, 8 Dec 2015 12:37:19 GMT (10kb)
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