Geodesic
Splitting of perturbated differential operators with unbounded operator coefficients
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 1-16.

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We obtain some theorems on splitting of differential operators of the form $$ \mathcal L=\frac{d}{dt}-A_0-BA_0^\nu\colon\, D(\mathcal L)\subset C(\mathbb R,\mathcal Y)\to C(\mathbb R,\mathcal Y) $$ acting in the Banach space $C(\mathbb R,\mathcal Y)$ of continuous and bounded functions defined on real axis $\mathbb R$ with values in the Banach space $\mathcal Y$. The linear operator $A_0\colon\,D(A_0)\subset\mathcal Y\to\mathcal Y$ is the generating operator of a strongly continuous semigroup of operators and its spectrum does not intersect the imaginary axis $i\mathbb R$. Here $A_0^\nu$, $\nu\in[0,1)$, is a fractional power of $A_0$ and $B\colon\,C(\mathbb R,\mathcal Y)\to C(\mathbb R,\mathcal Y)$ is a bounded linear operator. 
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A. G. Baskakov. Splitting of perturbated differential operators with unbounded operator coefficients. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a0/

[1] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[2] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[3] Fridrikhs K. O., Vozmuschenie spektra operatorov v gilbertovom prostranstve, Mir, M., 1969

[4] Bortei M. S., Fodchuk V. I., “O privodimosti i postroenii reshenii sistem lineinykh differentsialnykh uravnenii s kvaziperiodicheskimi koeffitsientami”, Differents. uravn., 15:5 (1979), 771–783 | MR | Zbl

[5] Fomin V. N., Matematicheskaya teoriya parametricheskogo rezonansa v lineinykh raspredelennykh sistemakh, Izd-vo LGU, Leningrad, 1972 | MR

[6] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, Izd-vo VGU, Voronezh, 1987 | MR | Zbl

[7] Baskakov A. G., “O rasscheplenii differentsialnogo operatora s neogranichennymi operatornymi koeffitsientami”, DAN, 323:3 (1992), 380–384 | MR | Zbl

[8] Aksenov A. A., Diss. $\dots$ k.f.-m.n., Voronezh, 1989

[9] Krein S. G., “Asimptoticheskoe rasscheplenie operatornykh uravnenii”, Funktsii Lyapunova i ikh primeneniya, Nauka, Novosibirsk, 1986, 206–214 | MR

[10] Kopachevskii N. D., Krein S. G., Ngo Zui Kan, Operatornye metody v lineinoi gidrodinamike, Nauka, M., 1989 | MR | Zbl

[11] Baskakov A. G., “Polugruppy raznostnykh operatorov v spektralnom analize lineinykh differentsialnykh operatorov”, Funkts. anal. i ego prilozhen., 30:3 (1996), 1–11 | MR | Zbl

[12] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR

[13] Baskakov A. G., “Teorema o rasscheplenii operatorov i nekotorye smezhnye voprosy analiticheskoi teorii vozmuschenii”, Izv. AN SSSR. Ser. matem., 50:3 (1986), 435–457 | MR | Zbl

[14] Danford N., Shvarts Dzh. T., Lineinye operatory, T. III, Mir, M., 1974