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Lyapunov theorems for Banach spaces


Authors: Yu. Latushkin and S. Montgomery-Smith
Journal: Bull. Amer. Math. Soc. 31 (1994), 44-49
MSC: Primary 47D06; Secondary 34D05, 34D20, 34G10, 47N20
DOI: https://doi.org/10.1090/S0273-0979-1994-00495-1
MathSciNet review: 1249356
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Abstract: We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for E-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.

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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1994-00495-1
Keywords: Hyperbolicity, evolution family, exponential dichotomy, weighted composition operators, spectral mapping theorem
Article copyright: © Copyright 1994 American Mathematical Society

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