Geodesic
The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 109-140.

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In this work we present the operators Aγ = γA + -γA with Re γ = 1/2 in the case of an operator A from the class of nondissipative operators generating nonselfadjoint curves, whose correlation functions have a limit as t → ±∞. The asympthotics of the stationary curves e^(itAγ)f as t → ±∞ onto the absolutely continuous subspace of Aγ are obtained. These asymptotics and the obtained asymptotics in [9] of the nondissipative curves e^(itA)f allow to construct the scattering theory for the couples (Aγ , A) and (A, Aγ). We consider the basic terms from the scattering theory - wave operators, a scattering operator and the question of a similarity of A and Aγ. We obtain explicitly the wave operators, the scattering operator and the similarity of A and Aγ.
Keywords: Operator Colligation, Nondissipative Curve, Correlation Function, Wave Operator, Scattering Operator 
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     author = {Borisova, Galina},
     title = {The {Operators} {A\ensuremath{\gamma}} = {\ensuremath{\gamma}A} + {-\ensuremath{\gamma}A} for a {Class} of {Nondissipative} {Operators} {A} with a {Limit} of the {Corresponding} {Correlation} {Function}},
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Borisova, Galina. The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function. Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 109-140. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a1/