Geodesic
The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
Serdica Mathematical Journal, Tome 29 (2003) no. 2, pp. 109-140 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

Voir la notice de l'article

In 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.
Keywords: Operator Colligation, Nondissipative Curve, Correlation Function, Wave Operator, Scattering Operator 
@article{SMJ2_2003_29_2_a1,
     author = {Borisova, Galina},
     title = {The {Operators} {A\ensuremath{\gamma}} = {\ensuremath{\gamma}A} + {-\ensuremath{\gamma}A} for a {Class} of {Nondissipative} {Operators} {A} with a {Limit} of the {Corresponding} {Correlation} {Function}},
     journal = {Serdica Mathematical Journal},
     pages = {109--140},
     year = {2003},
     volume = {29},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a1/}
}
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
SP  - 109
EP  - 140
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a1/
LA  - en
ID  - SMJ2_2003_29_2_a1
ER  - 
%0 Journal Article
%A Borisova, Galina
%T The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
%J Serdica Mathematical Journal
%D 2003
%P 109-140
%V 29
%N 2
%U http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a1/
%G en
%F SMJ2_2003_29_2_a1
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, Tome 29 (2003) no. 2, pp. 109-140. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_2_a1/