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Title: The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
Authors: Borisova, Galina
Keywords: Operator Colligation
Nondissipative Curve
Correlation Function
Wave Operator
Scattering Operator
Issue Date: 2003
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 29, No 2, (2003), 109p-140p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12
ISSN: 1310-6600
Appears in Collections:Volume 29 Number 2

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