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

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 2, page 109-140
- ISSN: 1310-6600

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topBorisova, 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 -

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