Geodesic
Linear functional differential equations in space with unindefinite metric
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 48-49.

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We study the spectral properties of operator generating unindefinite metric of state space for linear functional differential equation. The results can find application in the theory of canonical decompositions of functional differential equations.
Keywords: linear functional differential equation, indefinite metric, canonical decomposition of functional differential equation. 
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Yu. F. Dolgii; D. S. Bykov. Linear functional differential equations in space with unindefinite metric. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 48-49. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a19/

[1] Krasovskii N.N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959, 550 pp.

[2] Shimanov S.N., “K teorii lineinykh differentsialnykh uravnenii s posledeistviem”, Differentsialnye uravneniya, 1:1 (1965), 102–116 | MR | Zbl

[3] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984, 421 pp.

[4] Osipov Yu.S., “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 605–618 | MR

[5] Bykov D.S., Dolgii Yu.F., “Kanonicheskie approksimatsii v zadache optimalnoi stabilizatsii avtonomnykh sistem s posledeistviem”, Trudy Instituta matematiki i mekhaniki UrO RAN, 17:2 (2011), 20–34

[6] Pontryagin L.S., “Ermitovy operatory v prostranstvakh s indefinitnoi metrikoi”, Izv. AN SSSR. Ser. matem., 8 (1944), 243–280 | MR | Zbl

[7] Iokhvidov I.S., Krein M.G., “Spektralnaya teoriya operatorov v prostranstvakh s indefinitnoi metrikoi. I”, Tr. Mosk. mat. o–va, 5, 1956, 367–432 | MR | Zbl

[8] Azizov T.Ya., Iokhvidov I.S., Osnovy teorii lineinykh operatorov v prostranstvakh s indefinitnoi metrikoi, Nauka, M., 1986, 353 pp.