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Russian Mathematical Surveys, 2016, Volume 71, Issue 3, Pages 391–415
DOI: https://doi.org/10.1070/RM9708 (Mi rm9708) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Dispersion estimates for one-dimensional Schrödinger and Klein–Gordon equations revisited

I. E. Egorovaa, E. A. Kopylovabc, V. A. Marchenkoa, G. Teschldc

a B. Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
c University of Vienna, Vienna, Austria
d International Erwin Schrödinger Institute for Mathematical Physics, Vienna, Austria
English version PDF (643 kB) Citations (20)
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DOI: https://doi.org/10.1070/RM9708
Abstract: It is shown that for a one-dimensional Schrödinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrödinger and Klein–Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum.
Bibliography: 29 titles.
Keywords: Schrödinger equation, Klein–Gordon equation, dispersion estimates, scattering.
Funding agency Grant number
Austrian Science Fund Y330
P27492-N25
Research supported by the Austrian Science Fund (FWF) under grants Y330 and P27492-N25.
Received: 21.12.2015
Russian version:
Uspekhi Matematicheskikh Nauk, 2016, Volume 71, Issue 3(429), Pages 3–26
DOI: https://doi.org/10.4213/rm9708
Bibliographic databases:
Document Type: Article
UDC: 517.955+517.958
MSC: Primary 35L10, 34L25; Secondary 81U30, 81Q15
Language: English
Original paper language: Russian
Citation: I. E. Egorova, E. A. Kopylova, V. A. Marchenko, G. Teschl, “Dispersion estimates for one-dimensional Schrödinger and Klein–Gordon equations revisited”, Uspekhi Mat. Nauk, 71:3(429) (2016), 3–26; Russian Math. Surveys, 71:3 (2016), 391–415
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
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    References:68
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