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Title: Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators
Authors: Kirchev, Kiril
Borisova, Galina
Keywords: Unbounded Operator
Operator Colligation
Characteristic Function
Nondissipative Curve
Correlation Function
Wave Operator
Scattering Operator
Issue Date: 2005
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 31, No 1-2, (2005), 95p-174p
Abstract: In this paper classes of K^r -operators are considered – the classes of bounded and unbounded operators A with equal domains of A and A*, finite dimensional imaginary parts and presented as a coupling of a dissipative operator and an antidissipative one with real absolutely continuous spectra and the class of unbounded dissipative K^r -operators A with different domains of A and A* and with real absolutely continuous spectra. Their triangular models are presented. The asymptotics of the corresponding continuous curves with generators from these classes are obtained in an explicit form. With the help of the obtained asymptotics the scattering theory for the couples (A*, A) when A belongs to the introduced classes is constructed.
Description: 2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.
ISSN: 1310-6600
Appears in Collections:Volume 31 Number 1-2

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