Geodesic
Estimates for the Green's function and parameters of~exponential dichotomy of a~hyperbolic operator semigroup and linear relations
Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1049-1086

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By applying Lyapunov's equation, the method of similar operators, and the methods of harmonic analysis, we obtain estimates for the parameters of exponential dichotomy and for the Green's function constructed for a hyperbolic operator semigroup and a hyperbolic linear relation. Estimates are obtained using quantities which are determined by the resolvent of the infinitesimal operator of the operator semigroup and of the linear relation. Bibliography: 51 titles.
Keywords: hyperbolic operator semigroup, linear relations, method of similar operators, Lyapunov's equation, spectrum of an operator. 
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     title = {Estimates for the {Green's} function and parameters of~exponential dichotomy of a~hyperbolic operator semigroup and linear relations},
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A. G. Baskakov. Estimates for the Green's function and parameters of~exponential dichotomy of a~hyperbolic operator semigroup and linear relations. Sbornik. Mathematics, Tome 206 (2015) no. 8, pp. 1049-1086. http://geodesic.mathdoc.fr/item/SM_2015_206_8_a1/