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.
