This article is cited in 26 papers

The existence of wave operators in scattering theory for pairs of spaces

A. L. Belopol'skii, M. Sh. Birman


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.

UDC: 517.9

MSC: 47A40, 47B25, 47A55

Received: 20.03.1968

 English version: Mathematics of the USSR-Izvestiya, 1968, 2:5, 1117–1130

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