|
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
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.
Received: 21.12.2015
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
Linking options:
https://www.mathnet.ru/eng/rm9708https://doi.org/10.1070/RM9708 https://www.mathnet.ru/eng/rm/v71/i3/p3
|
Statistics & downloads: |
Abstract page: | 611 | Russian version PDF: | 188 | English version PDF: | 14 | References: | 68 | First page: | 49 |
|