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

Kirchev, Kiril; Borisova, Galina

Serdica Mathematical Journal (2005)

- Volume: 31, Issue: 1-2, page 95-174
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topKirchev, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.