Exponential expansiveness and complete admissibility for evolution families
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 739-749
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Connections between uniform exponential expansiveness and complete admissibility of the pair $(c_0({\mathbb N}, X),c_0({\mathbb N}, X))$ are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.
Connections between uniform exponential expansiveness and complete admissibility of the pair $(c_0({\mathbb N}, X),c_0({\mathbb N}, X))$ are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.
Classification : 34D05, 34E05, 34G99
Keywords: evolution family; uniform exponential expansiveness; complete admissibility
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Megan, Mihail; Sasu, Bogdan; Sasu, Adina Luminiţa. Exponential expansiveness and complete admissibility for evolution families. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 739-749. http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a15/

[1] A. Ben-Artzi, I.  Gohberg and M. A. Kaashoek: Invertibility and dichotomy of differential operators on the half-line. J.  Dynam. Differential Equations 5 (1993), 1–36. | DOI | MR

[2] C.  Chicone and Y. Latushkin: Evolution Semigroups in Dynamical Systems and Differential Equations. Math. Surveys and Monographs, Vol. 70. Amer. Math. Soc., , 1999. | DOI | MR

[3] S. N. Chow and H.  Leiva: Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces. J. Differential Equations 120 (1995), 429–477. | DOI | MR

[4] J. Daleckii and M. G. Krein: Stability of Solutions of Differential Equations in Banach Spaces. Trans. Math. Monographs 43. AMS, Providence, 1974. | MR

[5] D. Henry: Geometric Theory of Semilinear Parabolic Equations. Springer-Verlag, New York, 1981. | MR | Zbl

[6] Y.  Latushkin and T.  Randolph: Dichotomy of differential equations on Banach spaces and algebra of weighted translation operators. Integral Equations Operator Theory 23 (1995), 472–500. | DOI | MR

[7] Y. Latushkin and R. Schnaubelt: Evolution semigroups, translation algebras and exponential dichotomy of cocycles. J.  Differential Equations 159 (1999), 321–369. | DOI | MR

[8] M. Megan, A. L. Sasu and B.  Sasu: On uniform exponential stability of periodic evolution operators in Banach spaces. Acta Math. Univ. Comenian. 69 (2000), 97–106. | MR

[9] M.  Megan, A. L.  Sasu and B. Sasu: On uniform exponential stability of linear skew-product semiflows in Banach spaces. Bull. Belg. Math. Soc. Simon Stevin 9 (2002), 143–154. | DOI | MR

[10] M.  Megan, A. L. Sasu and B. Sasu: Discrete admissibility and exponential dichotomy for evolution families. Discrete Contin. Dynam. Systems 9 (2003), 383–397. | MR

[11] M.  Megan, B.  Sasu and A. L. Sasu: On nonuniform exponential dichotomy of evolution operators in Banach spaces. Integral Equations Operator Theory 44 (2002), 71–78. | DOI | MR

[12] N. Van Minh, F.  Räbiger and R.  Schnaubelt: Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line. Integral Equations Operator Theory 32 (1998), 332–353. | DOI | MR

[13] A.  Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR | Zbl

[14] V. A. Pliss and G. R.  Sell: Robustness of exponential dichotomies in infinite-dimensional dynamical systems. J.  Dynam. Differential Equations 3 (1999), 471–513. | MR