Geodesic
Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 18-25.

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The spectral properties of operators constructed from a family of evolution operators are studied in Banach spaces of vector functions defined by a weight function of pre-exponential growth. Necessary and sufficient conditions for the invertibility of such operators are obtained in terms of exponential dichotomy. We prove a spectrum mapping theorem for semigroups of Howland difference operators generated by the operator under study.
Keywords: differential operator, weighted spaces of functions, spectral properties of operators, evolution operator, exponential dichotomy, Howland difference operator, Banach space, spectrum mapping theorem. 
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M. S. Bichegkuev. Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 18-25. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/

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