Geodesic
Conditions for the range of a difference operator to be closed
Izvestiya. Mathematics, Tome 61 (1997) no. 3, pp. 593-618 
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/
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     title = {Conditions for the range of a~difference operator to be closed},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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