Preda, Petre; Megan, Mihail Exponential dichotomy of evolutionary processes in Banach spaces. (English) Zbl 0609.47051 Czech. Math. J. 35(110), 312-323 (1985). 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 Cited in 4 ReviewsCited in 12 Documents MSC: 47D03 Groups and semigroups of linear operators 34G10 Linear differential equations in abstract spaces Keywords:uniform exponential dichotomy for a linear evolutionary process in a Banach space; R. Datko’s characterization of the uniform exponential stability Citations:Zbl 0243.34107; Zbl 0241.34071 PDFBibTeX XMLCite \textit{P. Preda} and \textit{M. Megan}, Czech. Math. J. 35(110), 312--323 (1985; Zbl 0609.47051) Full Text: DOI EuDML References: [1] E. A. Barbašin: Introduction in the theory of stability. Izd. Nauka, Moscow, 1967) [2] R. Conti: On the boundedness of solutions of ordinary differential equations. Funkcial. Ekvac. 9(1966), 23-26. · Zbl 0152.08401 [3] W. A. Coppel: Stability and asymptotic behaviour of differential equations. D.C. Heath, Boston, 1965. · Zbl 0154.09301 [4] R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space. Siam J. Math. Anal., 3 (1973), 428-445. · Zbl 0241.34071 · doi:10.1137/0503042 [5] D. L. Lovelady: Boundedness properties for linear ordinary differential equations. Proc. Amer. Math. Soc., 41 (1973), 193-196. · Zbl 0246.34018 · doi:10.2307/2038839 [6] J. L. Massera J. J. Schäffer: Linear differential equations and function spaces. Academic Press, New York and London, 1966. · Zbl 0243.34107 [7] M. Megan P. Preda: On exponential dichotomy in Banach spaces. Bull. Austral. Math. Soc., 23( 1981), 293–306. · Zbl 0459.34037 · doi:10.1017/S0004972700007140 [8] P. Preda M. Megan: An extension of a theorem of R. Datko. preprint in Seminarul de Teoria Structurilor, Univ. Timişoara, 32 (1982), 1-12. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.