Geodesic
Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators
Serdica Mathematical Journal, Tome 31 (2005) no. 1-2, pp. 95-174.

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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.
Keywords: Unbounded Operator, Operator Colligation, Characteristic Function, Nondissipative Curve, Correlation Function, Wave Operator, Scattering Operator 
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     title = {Triangular {Models} and {Asymptotics} of {Continuous} {Curves} with {Bounded} and {Unbounded} {Semigroup} {Generators}},
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Kirchev, Kiril; Borisova, Galina. Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators. Serdica Mathematical Journal, Tome 31 (2005) no. 1-2, pp. 95-174. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_1-2_a3/