Invertibility of almost periodic $c$-continuous functional operators
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 431-446 Cet article a éte moissonné depuis la source Math-Net.Ru

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Statements are proved about the invertibility of operators $\frac{d^m}{dt^m}+A$ ($m$ a positive integer) and $B$ acting in the space of bounded vector-valued functions on $(-\infty,\infty)$ and in the space of bounded vector-valued functions on a countable Abelian group, respectively. Bibliography: 25 titles.
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     title = {Invertibility of almost periodic $c$-continuous functional operators},
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V. E. Slyusarchuk. Invertibility of almost periodic $c$-continuous functional operators. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 431-446. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a1/

[1] Mukhamadiev E., “Ob obratimosti differentsialnykh operatorov v prostranstve nepreryvnykh i ogranichennykh na osi funktsii”, DAN SSSR, 196:1 (1971), 47–49 | Zbl

[2] Mukhamadiev E., “Ob obratimosti funktsionalnykh operatorov v prostranstve ogranichennykh na osi funktsii”, Matem. zametki, 11:3 (1972), 269–274 | Zbl

[3] Kolesov Yu. S., “Neobkhodimye i dostatochnye usloviya eksponentsialnoi dikhotomii reshenii lineinykh pochti periodicheskikh uravnenii s posledeistviem”, Vestnik YaGU, 1973, no. 5, 28–62 | MR

[4] Kolesov Yu. S., “Obzor rezultatov po teorii ustoichivosti reshenii differentsialno-ravnostnykh uravnenii s pochti periodicheskimi koeffitsientami”, Issledovaniya po ustoichivosti v teorii kolebanii, Yaroslavl, 1977, 82–141 | MR

[5] Mukhamadiev E., “Ob obratimosti differentsialnykh operatorov v chastnykh proizvodnykh ellipticheskogo tipa”, DAN SSSR, 205:6 (1972), 1292–1295

[6] Shubin M. A., “Pochti periodicheskie funktsii i differentsialnye operatory s chastnymi proizvodnymi”, UMN, XXVIII:2 (1978), 3–47

[7] Favard J., “Sur les équations différentielles à coefficients presque-périodiqies”, Acta math., 51 (1927), 31–81 | DOI | MR | Zbl

[8] Levitan B. M., Pochti-periodicheskie funktsii, Gostekhizdat, M., 1953

[9] Amerio L., “Soluzioni quasi-periodiche, o limitate, di sistemi differenziali non lineari quazi-periodici, o limitati”, An. mat. pura et appl., 39 (1975), 97–119 | DOI | MR

[10] Zhikov V. V., “Ob odnom dopolnenii k klassicheskoi teorii Favara”, Matem. zametki, 7:2 (1970), 239–246

[11] Zhikov V. V., “Suschestvovanie pochti periodicheskikh po Levitanu reshenii lineinykh sistem (2-e dopolnenie k klassicheskoi teorii Favara)”, Matem. zametki, 9:4 (1971), 409–414 | Zbl

[12] Zhikov V. V., Levitan B. M., “Teoriya Favara”, UMN, XXXII:2 (1977), 123–172

[13] Lyubarskii M. G., “Rasprostranenie teorii Favara na sluchai sistem lineinykh differentsialnykh uravnenii s neogranichennymi pochti periodicheskimi po Levitanu koeffitsientami”, DAN SSSR, 2:4 (1972), 808–810

[14] Fink A. M., “Semi-separated conditions for almost periodic solutions”, J. Diff. Equat., 11 (1972), 245–251 | DOI | MR | Zbl

[15] Krasnoselskii M. A., Burd V. Sh., Kolesov Yu. S., Nelineinye pochti periodicheskie kolebaniya, Nauka, M., 1970 | MR

[16] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971 | MR

[17] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[18] Slyusarchuk V. E., “Obratimost funktsionalno-differentsialnykh operatorov”, DAN USSR, ser. A, 1980, no. 9, 29–32 | MR

[19] Pontryagin L. S., Nepreryvnye gruppy, Gostekhizdat, M., 1954 | MR

[20] Slyusarchuk V. E., “Obratimost pochti periodicheskikh operatorov, porozhdennykh diskretnymi sistemami”, Ukr. matem. zh., 31:4 (1979), 460–463 | MR | Zbl

[21] Slyusarchuk V. E., “Ob ogranichennykh i pochti periodicheskikh resheniyakh neyavnykh raznostnykh uravnenii v banakhovom prostranstve”, DAN USSR, ser. A, 1975, no. 6, 503–509

[22] Slyusarchuk V. E., “Obobschenie teoremy Vinera ob absolyutno skhodyaschikhsya ryadakh Fure i ego primenenie k issledovaniyu beskonechnomernykh diskretnykh sistem”, Izv. AN BSSR, ser. fiz.-matem. nauk, 1977, no. 2, 23–26 | Zbl

[23] Slyusarchuk V. E., “Spektry nekotorykh operatorov v prostranstve ogranichennykh vektor-funktsii”, Topologicheskie prostranstva i ikh otobrazheniya, no. 8, Riga, 1977, 113–122 | Zbl

[24] Slyusarchuk V. E., “Otsenki spektrov i obratimost funktsionalnykh operatorov”, Matem. sb., 105 (147) (1978), 268–285

[25] Slyusarchuk V. E., “Reshenie lineinykh funktsionalnykh uravnenii v prostranstve ogranichennykh na $R^n$ funktsii”, Ukr. matem. zh., 30:3 (1978), 416–422 | MR | Zbl