Exponential dichotomy of evolutionary processes in Banach spaces. (English) Zbl 0609.47051

The authors characterize the uniform exponential dichotomy for a linear evolutionary process in a Banach space, generalizing a similar result of J. L. Massera and J. J. Schäffer [Linear differential equations and function spaces (1966; Zbl 0243.34107)] for an evolutionary process generated by a differential equation. As a particular case they also obtain R. Datko’s characterization of the uniform exponential stability [see SIAM J. Math. Anal. 3, 428-445 (1973; Zbl 0241.34071)].
Reviewer: G.Di Blasio


47D03 Groups and semigroups of linear operators
34G10 Linear differential equations in abstract spaces
Full Text: EuDML


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