Abstract:
Existence conditions are considered for wave operators for pairs of self-adjoint operators which act in different Hilbert spaces. The “operator of identification” is not assumed to be isometric. The existence criteria obtained for wave operators (local and nonlocal) are related to perturbation theory of nuclear operators. The construction of wave operators is carried out by a stationary method.
Citation:
A. L. Belopol'skii, M. Sh. Birman, “The existence of wave operators in scattering theory for pairs of
spaces”, Math. USSR-Izv., 2:5 (1968), 1117–1130
\Bibitem{BelBir68}
\by A.~L.~Belopol'skii, M.~Sh.~Birman
\paper The existence of wave operators in scattering theory for pairs of
spaces
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1117--1130
\mathnet{http://mi.mathnet.ru/eng/im2511}
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000712}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=238101}
\zmath{https://zbmath.org/?q=an:0183.41901|0186.20803}
Linking options:
https://www.mathnet.ru/eng/im2511
https://doi.org/10.1070/IM1968v002n05ABEH000712
https://www.mathnet.ru/eng/im/v32/i5/p1162
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