Geodesic
About reversibility states of linear differential operators with periodic unbounded operator coefficients
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 136-144.

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For investigated linear differential operator (equation) with unbounded periodic operator coefficients defined at one of the Banach space of vector functions defined on all real axis difference operator (equation) with constant operator coefficient defined at appropriate Banach space of two-side vector sequences is considered. For differential and difference operators propositions about kernel and co-image dimensions coincidence, simultaneous complementarity of kernels and images, simultaneous reversibility, spectrum interrelation are proved. 
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V. B. Didenko. About reversibility states of linear differential operators with periodic unbounded operator coefficients. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 136-144. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a2/

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