Geodesic
On invertibility states of differential and difference operators
Izvestiya. Mathematics , Tome 82 (2018) no. 1, pp. 1-13.

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To every differential operator with unbounded operator coefficients we assign a difference operator in a space of bounded sequences. We prove the coincidence of the invertibility states of these operators (this means that the properties of the images and kernels of these operators coincide). We give a general scheme for proving the coincidence of the invertibility states of two abstract operators.
Keywords: invertibility states, Fredholm property, family of evolution operators, differential operator, difference operator. 
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A. G. Baskakov; V. B. Didenko. On invertibility states of differential and difference operators. Izvestiya. Mathematics , Tome 82 (2018) no. 1, pp. 1-13. http://geodesic.mathdoc.fr/item/IM2_2018_82_1_a0/

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