Spectral analysis of linear relations and degenerate operator semigroups
Sbornik. Mathematics, Tome 193 (2002) no. 11, pp. 1573-1610 Cet article a éte moissonné depuis la source Math-Net.Ru

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Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups.
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A. G. Baskakov; K. I. Chernyshov. Spectral analysis of linear relations and degenerate operator semigroups. Sbornik. Mathematics, Tome 193 (2002) no. 11, pp. 1573-1610. http://geodesic.mathdoc.fr/item/SM_2002_193_11_a0/

[1] Cross R., Multivalued linear operators, M. Dekker, New York, 1998 | MR | Zbl

[2] Favini A., Yagi A., Degenerate differential equations in Banach spaces, Monogr. Textbooks Pure Appl. Math., 215, M. Dekker, New York, 1998

[3] Ritsner V. S., Teoriya lineinykh otnoshenii, Dep. v VINITI, 846–82, 1982

[4] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[5] Danford N., Shvarts Dzh. T., Lineinye operatory. T. I. Obschaya teoriya, IL, M., 1962

[6] von Neumann J., “Über adjungierte Funktionaloperatoren”, Ann. of Math. (2), 33 (1932), 294–310 | DOI | MR | Zbl

[7] Arendt W., “Approximation of degenerate semigroups”, Tübinger Berichte zur Funktionalanalysis, 9 (1999/2000), 33–46 | MR

[8] S. G. Krein (red.), Funktsionalnyi analiz, SMB, Nauka, M., 1972 | MR

[9] Baskakov A. G., Chernyshov K. I., “Uporyadochennye pary operatorov i polugruppy”, Izv. RAEN. MMMIU, 2:3 (1998), 39–69

[10] Baskakov A. G., Chernyshov K. I., “Postroenie fazovogo prostranstva i reshenii lineinykh uravnenii, ne razreshennykh otnositelno proizvodnoi”, Dokl. RAN, 371:3 (2000), 295–298 | MR | Zbl

[11] Sviridyuk G. A., Fedorov V. E., “O edinitsakh analiticheskikh polugrupp operatorov s yadrami”, Sib. matem. zhurn., 39:3 (1998), 604–616 | MR

[12] Fedorov V. E., “Vyrozhdennye silno nepreryvnye polugruppy operatorov”, Algebra i analiz, 12:3 (2000), 173–200 | MR

[13] Melnikova I. V., Gladchenko A. V., “Korrektnost zadachi Koshi dlya vklyuchenii v banakhovykh prostranstvakh”, Dokl. RAN, 361:6 (1998), 736–739 | MR | Zbl

[14] Engel K.-J., Nagel R., One-parameter semigroups for linear evolution equations, Grad. Texts in Math., 194, Springer-Verlag, New York, 2000 | MR

[15] Räbiger F., Wolff M. P. H., “Spectral and asymptotic properties of resolvent-dominated operators”, Tübinger Berichte zur Funktionalanalysis, 7 (1997/1998), 217–235

[16] Burbaki N., Spektralnaya teoriya, Mir, M., 1972 | MR | Zbl

[17] Favini A., Yagi A., “Multivalued linear operators and degenerate evolution equations”, Ann. Mat. Pura Appl. (4), 163 (1993), 353–384 | DOI | MR | Zbl

[18] Baskakov A. G., Chernyshov K. I., “Ob usloviyakh kompaktnosti spektra uporyadochennykh par lineinykh operatorov”, Izv. RAEN. MMMIU, 3:3 (1999), 5–24 | MR | Zbl

[19] Pich A., Operatornye idealy, Mir, M., 1982 | MR

[20] Baskakov A. G., “Operatornye ergodicheskie teoremy i dopolnyaemost podprostranstv banakhovykh prostranstv”, Izv. vuzov. Ser. matem., 11(318) (1988), 3–11 | MR | Zbl

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

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

[23] Radbel N. I., Uporyadochennye pary lineinykh operatorov i zadacha Koshi dlya uravneniya $A\dot x(t)+Bx(t)=0$ v banakhovom prostranstve, Diss. ...kand. fiz.-mat. nauk, IPMiM, Donetsk, 1984

[24] Rutkas A. G., “Zadacha Koshi dlya uravneniya $A\dot x(t)+Bx(t)=f(t)$”, Differents. uravneniya, 11:11 (1975), 1996–2010 | MR | Zbl

[25] Chernyshov K. I., Ob operatornykh differentsialnykh uravneniyakh, ne razreshennykh otnositelno proizvodnoi, Diss. ...kand. fiz.-mat. nauk, IM AN USSR, Kiev, 1979

[26] Krein S. G., Chernyshov K. I., “Singulyarno vozmuschennye differentsialnye uravneniya v banakhovom prostranstve”, IX Mezhdunarodnaya konf. po nelineinym kolebaniyam, T. 1, Nauk. dumka, Kiev, 1984, 193–197 | MR

[27] Ditkin V. V., “O nekotorykh spektralnykh svoistvakh puchka lineinykh ogranichennykh operatorov”, Matem. zametki, 31:1 (1982), 75–79 | MR | Zbl

[28] Sviridyuk G. A., “K obschei teorii polugrupp operatorov”, UMN, 49:4 (1994), 47–74 | MR | Zbl

[29] Baskakov A. G., Chernyshov K. I., “Ergodic subspaces and analytic semigroups”, Spectral and evolutionary problems, Proc. of the Eleventh Crimean Autumn Math. School, 11, National Taurida V. Vernadsky Univ., Simferopol, 2001, 136–143 | MR