Geodesic
Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 85-89 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $A$ and $A_0$ be linear continuously invertible operators on a Hilbert space $\mathfrak{H}$ such that $A^{-1}-A_0^{-1}$ has finite rank. Assuming that $\sigma(A_0)=\varnothing$ and that the operator semigroup $V_+(t)=\exp\{iA_0t\}$, $t\ge0$, is of class $C_0$, we state criteria under which the semigroups $U_\pm(t)=\exp\{\pm iAt\}$, $t\ge0$, are of class $C_0$ as well. The analysis in the paper is based on functional models for nonself-adjoint operators and techniques of matrix Muckenhoupt weights.
Keywords: nonself-adjoint operator, perturbation of a semigroup, functional model, Muckenhoupt condition. 
@article{FAA_2008_42_3_a10,
     author = {G. M. Gubreev and Yu. D. Latushkin},
     title = {Perturbations of {Strongly} {Continuous} {Operator} {Semigroups,} and {Matrix} {Muckenhoupt} {Weights}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {85--89},
     year = {2008},
     volume = {42},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/}
}
TY  - JOUR
AU  - G. M. Gubreev
AU  - Yu. D. Latushkin
TI  - Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2008
SP  - 85
EP  - 89
VL  - 42
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/
LA  - ru
ID  - FAA_2008_42_3_a10
ER  - 
%0 Journal Article
%A G. M. Gubreev
%A Yu. D. Latushkin
%T Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2008
%P 85-89
%V 42
%N 3
%U http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/
%G ru
%F FAA_2008_42_3_a10
G. M. Gubreev; Yu. D. Latushkin. Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 85-89. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a10/

[1] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[2] S. Treil, A. Volberg, J. Funct. Anal., 143:2 (1997), 269–308 | DOI | MR | Zbl

[3] V. Sekefalvi-Nad, Ch. Foyash, Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[4] J. Delsarte, J. Math. Pures Appl., 14 (1935), 403–453 | Zbl

[5] M. S. Brodskii, M. S. Livshits, UMN, 13:1(79) (1958), 3–85 | MR | Zbl

[6] V. A. Zolotarev, Analiticheskie metody spektralnykh predstavlenii nesamosopryazhennykh i neunitarnykh operatorov, Iz-vo Kharkovskogo natsionalnogo universiteta im. Karazina, 2003