Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

Kirchev, Kiril, and Borisova, Galina. "Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators." Serdica Mathematical Journal 31.1-2 (2005): 95-174. <http://eudml.org/doc/219632>.

@article{Kirchev2005,
abstract = {2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.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.Partially supported by Grant MM-1403/04 of MESC and by Scientific Research Grants 19/13.03.2003 and 26/01.04.2004 of Shumen University.},
author = {Kirchev, Kiril, Borisova, Galina},
journal = {Serdica Mathematical Journal},
keywords = {Unbounded Operator; Operator Colligation; Characteristic Function; Nondissipative Curve; Correlation Function; Wave Operator; Scattering Operator; unbounded operator; operator colligation; characteristic function; nondissipative curve; correlation function; wave operator; scattering operator},
language = {eng},
number = {1-2},
pages = {95-174},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators},
url = {http://eudml.org/doc/219632},
volume = {31},
year = {2005},
}

TY - JOUR
AU - Kirchev, Kiril
AU - Borisova, Galina
TI - Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators
JO - Serdica Mathematical Journal
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 31
IS - 1-2
SP - 95
EP - 174
AB - 2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.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.Partially supported by Grant MM-1403/04 of MESC and by Scientific Research Grants 19/13.03.2003 and 26/01.04.2004 of Shumen University.
LA - eng
KW - Unbounded Operator; Operator Colligation; Characteristic Function; Nondissipative Curve; Correlation Function; Wave Operator; Scattering Operator; unbounded operator; operator colligation; characteristic function; nondissipative curve; correlation function; wave operator; scattering operator
UR - http://eudml.org/doc/219632
ER -