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Scattering theory for systems with different spatial asymptotics to the left and right
 COMMUN.MATH.PHYS. 63
, 1978
"... We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at ± oo, for example 2 4 V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x> 0). We then extend our results to higher dimensional systems periodic, except for a localised i ..."
Abstract

Cited by 40 (12 self)
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We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at ± oo, for example 2 4 V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x> 0). We then extend our results to higher dimensional systems periodic, except for a localised impurity, in all but one space dimension. A new method, "the twisting trick", is presented for proving the absence of singular continuous spectrum, and some independent applications of this trick are given in an appendix.
SCATTERING THEORY FOR DIFFRACTION GRATINGS#
, 1980
"... IAbstract. Scattering theory is developed for plane diffraction gratings. The author's theory of RayleighBloch wave expansions is used to construct wave operators and a scattering operator for such gratings. For gratings that admit no surface waves, transient wave fields near the gratings are ..."
Abstract
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IAbstract. Scattering theory is developed for plane diffraction gratings. The author's theory of RayleighBloch wave expansions is used to construct wave operators and a scattering operator for such gratings. For gratings that admit no surface waves, transient wave fields near the gratings are shown to behave for large times like free waves and corresponding asymptotic wave functions are calculated. These results are applied to analyze the echoes from gratings of signals due to localized sources. Finally, the echoes of sources remote from the grating are estimated and shown to be completely characterized by the Smatrix and the signal waveform. 0,.9 cessi es. I'., DD TAB3I ~ L