Geodesic
Conditions for the range of a~difference operator to be closed
Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 593-618.

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In this paper we study difference operators with variable differences that lie on a straight line in the space of holomorphic functions of a single variable. We obtain necessary and sufficient conditions for the range of such operators to be closed in terms of the zeros of their extreme coefficients. For a wide class of regions these conditions give simple criteria for the range of a difference operator to be closed. 
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S. G. Merzlyakov. Conditions for the range of a~difference operator to be closed. Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 593-618. http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a4/

[1] Merzlyakov S. G., “O zamknutosti obraza raznostnogo operatora”, DAN, 328:2 (1993), 141–142 | MR | Zbl

[2] Köte G., “Dualität in der Functionentheorie”, J. reine und angew. Math., 191:1–2 (1953), 30–49 | MR

[3] Merzlyakov S. G., “Invariantnye podprostranstva operatora edinichnogo sdviga”, Izv. RAN. Ser. matem., 56:6 (1992), 1244–1272 | MR | Zbl

[4] Edvards R., Funktsionalnyi analiz, Mir, M., 1969

[5] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[6] Merzlyakov S. G., “O vozmuschenii lineinykh operatorov v prostranstvakh golomorfnykh funktsii”, Matem. sb., 186:3 (1995), 103–130 | MR | Zbl

[7] Sebastyan-i-Silva Zh., “O nekotorykh klassakh lokalno vypuklykh prostranstv, vazhnykh v prilozheniyakh”, Matematika, 1:1 (1957), 60–77 | MR