The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

Borisova, Galina. "The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function." Serdica Mathematical Journal 29.2 (2003): 109-140. <http://eudml.org/doc/219553>.

@article{Borisova2003,
abstract = {2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12In this work we present the operators Aγ = γA + -γA with Re γ = 1/2 in the case of an operator A from the class of nondissipative operators generating nonselfadjoint curves, whose correlation functions have a limit as t → ±∞. The asympthotics of the stationary curves e^(itAγ)f as t → ±∞ onto the absolutely continuous subspace of Aγ are obtained. These asymptotics and the obtained asymptotics in [9] of the nondissipative curves e^(itA)f allow to construct the scattering theory for the couples (Aγ , A) and (A, Aγ). We consider the basic terms from the scattering theory - wave operators, a scattering operator and the question of a similarity of A and Aγ. We obtain explicitly the wave operators, the scattering operator and the similarity of A and Aγ.Partially supported by Grant MM-810/98 of MESC and by Scientific Research Grant 21/09.05.2001 of Shumen University.},
author = {Borisova, Galina},
journal = {Serdica Mathematical Journal},
keywords = {Operator Colligation; Nondissipative Curve; Correlation Function; Wave Operator; Scattering Operator; operator colligation; nondissipative curve; correlation function; wave operator; scattering operator},
language = {eng},
number = {2},
pages = {109-140},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function},
url = {http://eudml.org/doc/219553},
volume = {29},
year = {2003},
}

TY - JOUR
AU - Borisova, Galina
TI - The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
JO - Serdica Mathematical Journal
PY - 2003
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 29
IS - 2
SP - 109
EP - 140
AB - 2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12In this work we present the operators Aγ = γA + -γA with Re γ = 1/2 in the case of an operator A from the class of nondissipative operators generating nonselfadjoint curves, whose correlation functions have a limit as t → ±∞. The asympthotics of the stationary curves e^(itAγ)f as t → ±∞ onto the absolutely continuous subspace of Aγ are obtained. These asymptotics and the obtained asymptotics in [9] of the nondissipative curves e^(itA)f allow to construct the scattering theory for the couples (Aγ , A) and (A, Aγ). We consider the basic terms from the scattering theory - wave operators, a scattering operator and the question of a similarity of A and Aγ. We obtain explicitly the wave operators, the scattering operator and the similarity of A and Aγ.Partially supported by Grant MM-810/98 of MESC and by Scientific Research Grant 21/09.05.2001 of Shumen University.
LA - eng
KW - Operator Colligation; Nondissipative Curve; Correlation Function; Wave Operator; Scattering Operator; operator colligation; nondissipative curve; correlation function; wave operator; scattering operator
UR - http://eudml.org/doc/219553
ER -