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. 
@article{MZM_2014_95_1_a1,
     author = {M. S. Bichegkuev},
     title = {Spectral {Analysis} of {Differential} {Operators} with {Unbounded} {Operator} {Coefficients} in {Weighted} {Spaces} of {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {18--25},
     publisher = {mathdoc},
     volume = {95},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/}
}
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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/