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Volumn 193, Issue 1, 2002, Pages 116-139

Strong stability of bounded evolution families and semigroups

Author keywords

Carleman transform; Cauchy problem; Complete trajectory; Convolutions; Edge of the wedge; Evolution family; Evolution semigroup; Functional calculus; Nonautonomous; Semigroup; Stability

Indexed keywords


EID: 0036695950     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2001.3917     Document Type: Article
Times cited : (26)

References (37)
  • 1
    • 84966249611 scopus 로고
    • Tauberian theorems and stability of one-parameter semigroups
    • W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852.
    • (1988) Trans. Amer. Math. Soc , vol.306 , pp. 837-852
    • Arendt, W.1    Batty, C.J.K.2
  • 2
    • 0000503913 scopus 로고    scopus 로고
    • Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half line
    • W. Arendt and C. J. K. Batty, Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half line, Bull. London Math. Soc. 31 (1999), 291-304.
    • (1999) Bull. London Math. Soc , vol.31 , pp. 291-304
    • Arendt, W.1    Batty, C.J.K.2
  • 4
    • 0010600143 scopus 로고    scopus 로고
    • A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum
    • C. J. K. Batty, Z. Brzezniàk, and D. A. Greenfield, A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum, Studia Math. 121 (1996), 167-182.
    • (1996) Studia Math , vol.121 , pp. 167-182
    • Batty, C.J.K.1    Brzezniàk, Z.2    Greenfield, D.A.3
  • 6
    • 22044438651 scopus 로고    scopus 로고
    • Tauberian theorems and stability of solutions of the Cauchy problem
    • C. J. K. Batty, J. M. A. M. van Neerven, and F. Räbiger, Tauberian theorems and stability of solutions of the Cauchy problem, Trans. Amer. Math. Soc. 350 (1998), 2087-2103.
    • (1998) Trans. Amer. Math. Soc , vol.350 , pp. 2087-2103
    • Batty, C.J.K.1    van Neerven, J.M.A.M.2    Räbiger, F.3
  • 7
    • 0010532595 scopus 로고
    • Strong stability of Hilbert space contraction semigroups
    • K. N. Boyadzhiev and N. Levan, Strong stability of Hilbert space contraction semigroups, Stud. Sci. Math. Hung. 30 (1995), 165-182.
    • (1995) Stud. Sci. Math. Hung , vol.30 , pp. 165-182
    • Boyadzhiev, K.N.1    Levan, N.2
  • 8
    • 0003327379 scopus 로고    scopus 로고
    • "Evolution Semigroups in Dynamical Systems and Differential Equations"
    • Amer. Math. Soc., Providence, RI
    • C. Chicone and Y. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs, Vol. 70, Amer. Math. Soc., Providence, RI, 1999.
    • (1999) Mathematical Surveys and Monographs , vol.70
    • Chicone, C.1    Latushkin, Y.2
  • 9
    • 0001901179 scopus 로고    scopus 로고
    • Tauberian theorems for vector-valued Fourier and Laplace transforms
    • R. Chill, Tauberian theorems for vector-valued Fourier and Laplace transforms, Studia Math. 128 (1998), 55-69.
    • (1998) Studia Math , vol.128 , pp. 55-69
    • Chill, R.1
  • 11
    • 0034539508 scopus 로고    scopus 로고
    • Stability radius and internal versus external stability: An evolution semigroup approach
    • S. Clark, Y. Latushkin, S. Montgomery-Smith, and T. Randolph, Stability radius and internal versus external stability: An evolution semigroup approach, SIAM J. Control Optim. 38 (2000), 1757-1793.
    • (2000) SIAM J. Control Optim , vol.38 , pp. 1757-1793
    • Clark, S.1    Latushkin, Y.2    Montgomery-Smith, S.3    Randolph, T.4
  • 12
    • 84972562252 scopus 로고
    • Non-analytic functional calculi and spectral maximal spaces
    • P. C. Curtis and M. M. Neumann, Non-analytic functional calculi and spectral maximal spaces, Pacific J. Math. 137 (1989), 65-85.
    • (1989) Pacific J. Math , vol.137 , pp. 65-85
    • Curtis, P.C.1    Neumann, M.M.2
  • 13
    • 0001091909 scopus 로고
    • Uniform asymptotic stability of evolutionary processes in a Banach space
    • R. Datko, Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal. 3 (1972), 428-445.
    • (1972) SIAM J. Math. Anal , vol.3 , pp. 428-445
    • Datko, R.1
  • 14
    • 0000618712 scopus 로고
    • Lois "zero ou deux" pour les processus de Markov. Applications aux marches aléatoires
    • Y. Derriennic, Lois "zero ou deux" pour les processus de Markov. Applications aux marches aléatoires, Ann. Inst. Henri Poincaré n Sér. Sect. B 12 (1976), 111-129.
    • (1976) Ann. Inst. Henri Poincaré n Sér. Sect. B , vol.12 , pp. 111-129
    • Derriennic, Y.1
  • 15
    • 0003087399 scopus 로고
    • "Vector measures"
    • Mathematical Surveys, Providence, RI
    • J. Diestel and J. J. Uhl, "Vector measures." Mathematical Surveys, Vol. 15, Amer. Math. Soc., Providence, RI, 1977.
    • (1977) Amer. Math. Soc , vol.15
    • Diestel, J.1    Uhl, J.J.2
  • 16
    • 51649193023 scopus 로고
    • On the existence of a largest subharmonic minorant of a given function
    • Y. Domar, On the existence of a largest subharmonic minorant of a given function, Ark. Mat. 3 (1958), 429-440.
    • (1958) Ark. Mat , vol.3 , pp. 429-440
    • Domar, Y.1
  • 17
    • 0010566205 scopus 로고
    • Distributions and Fourier transforms
    • Academic Press, New York, London
    • W. F. Donoghue, Distributions and Fourier transforms, "Pure and Applied Mathematics," Vol. 32, Academic Press, New York, London, 1969.
    • (1969) "Pure and Applied Mathematics" , vol.32
    • Donoghue, W.F.1
  • 19
    • 38249016890 scopus 로고
    • Theorems of Katznelson-Tzafriri type for contractions
    • J. Esterle, E. Strouse, and F. Zouakia, Theorems of Katznelson-Tzafriri type for contractions, J. Funct. Anal. 94 (1990), 273-287.
    • (1990) J. Funct. Anal , vol.94 , pp. 273-287
    • Esterle, J.1    Strouse, E.2    Zouakia, F.3
  • 21
    • 0000364309 scopus 로고
    • Mittag-Leffler methods in the theory of Banach algebras and a new approach to Michael's problem
    • J. Esterle, Mittag-Leffler methods in the theory of Banach algebras and a new approach to Michael's problem, Contemp. Math. 32 (1984), 107-129.
    • (1984) Contemp. Math , vol.32 , pp. 107-129
    • Esterle, J.1
  • 22
    • 0010631276 scopus 로고
    • Non-analytic local functional calculus
    • C. Foias and F. H. Vasilescu, Non-analytic local functional calculus, Czechoslovak Math. J. 24(99) (1974), 270-283.
    • (1974) Czechoslovak Math. J , vol.24 , Issue.99 , pp. 270-283
    • Foias, C.1    Vasilescu, F.H.2
  • 23
    • 0010566895 scopus 로고
    • Bernstein's inequality from the point of view of operator theory
    • (translation from Vestnik Kharkov. Gos. Univ. 205 (1980) 77-105)
    • E. A. Gorin, Bernstein's inequality from the point of view of operator theory, Selecta Math. Soviet. 7 (1988), 191-219 (translation from Vestnik Kharkov. Gos. Univ. 205 (1980) 77-105).
    • (1988) Selecta Math. Soviet , vol.7 , pp. 191-219
    • Gorin, E.A.1
  • 24
    • 84966214397 scopus 로고
    • Bounded linear operators on Banach function spaces of vector-valued functions
    • N. E. Gretzky and J. J. Uhl, Bounded linear operators on Banach function spaces of vector-valued functions, Trans. Amer. Math. Soc. 167 (1972), 263-277.
    • (1972) Trans. Amer. Math. Soc , vol.167 , pp. 263-277
    • Gretzky, N.E.1    Uhl, J.J.2
  • 25
    • 85031436394 scopus 로고    scopus 로고
    • Deleted in proof
    • Deleted in proof.
  • 26
    • 0003730815 scopus 로고
    • "Topics in the Theory of Lifting"
    • Springer-Verlag, Berlin/Heidelberg/New York
    • A. Ionescu Tulcea and C. Ionescu Tulcea, "Topics in the Theory of Lifting," Springer-Verlag, Berlin/Heidelberg/New York, 1969.
    • (1969)
    • Ionescu Tulcea, A.1    Ionescu Tulcea, C.2
  • 27
    • 0010565775 scopus 로고
    • Classification of operators by means of their operational calculus
    • S. Kantorovitz, Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc. 115 (1965), 194-224.
    • (1965) Trans. Amer. Math. Soc , vol.115 , pp. 194-224
    • Kantorovitz, S.1
  • 29
    • 0003090139 scopus 로고
    • Asymptotic stability of linear differential equations in Banach spaces
    • Yu. I. Lyubich and Quôc Phong Vũ, Asymptotic stability of linear differential equations in Banach spaces, Studia Math. 88 (1988), 37-42.
    • (1988) Studia Math , vol.88 , pp. 37-42
    • Lyubich, Yu.I.1    Vũ, Q.P.2
  • 30
    • 0001459058 scopus 로고    scopus 로고
    • Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line
    • Nguyen 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.
    • (1998) Integral Equations Operator Theory , vol.32 , pp. 332-353
    • van Minh, N.1    Räbiger, F.2    Schnaubelt, R.3
  • 32
    • 0003518763 scopus 로고
    • "Evolutionary Integral Equations and Applications"
    • Birkhäuser Verlag, Basel
    • J. Prüss, "Evolutionary Integral Equations and Applications," Monographs in Mathematics, Birkhäuser Verlag, Basel, 1993.
    • (1993) Monographs in Mathematics
    • Prüss, J.1
  • 33
    • 0003348458 scopus 로고
    • "Equations of evolution"
    • Pitman, London/San Francisco/Melbourne
    • H. Tanabe, "Equations of evolution," Monographs and Studies in Mathematics, Vol. 6, Pitman, London/San Francisco/Melbourne, 1979.
    • (1979) Monographs and Studies in Mathematics , vol.6
    • Tanabe, H.1
  • 34
    • 0001598919 scopus 로고
    • Ideals in rings of analytic functions with smooth boundary values
    • B. A. Taylor and D. L. Williams, Ideals in rings of analytic functions with smooth boundary values, Canad. J. Math. 22 (1970), 1266-1283.
    • (1970) Canad. J. Math , vol.22 , pp. 1266-1283
    • Taylor, B.A.1    Williams, D.L.2
  • 35
    • 0010599638 scopus 로고    scopus 로고
    • A resolvent approach to stability of operator semigroups
    • Y. Tomilov, A resolvent approach to stability of operator semigroups, J. Operator Theory 46 (2001), 63-98.
    • (2001) J. Operator Theory , vol.46 , pp. 63-98
    • Tomilov, Y.1
  • 36
    • 0002411086 scopus 로고
    • On the spectrum, complete trajectories and asymptotic stability of linear semidynamical systems
    • Quôc Phong Vũ, On the spectrum, complete trajectories and asymptotic stability of linear semidynamical systems, J. Differential Equation 105 (1993), 30-45.
    • (1993) J. Differential Equation , vol.105 , pp. 30-45
    • Vũ, Q.P.1
  • 37
    • 0010631278 scopus 로고
    • Extension of analytic functions
    • F. Wolf, Extension of analytic functions, Duke Math. J. 14 (1947), 877-887.
    • (1947) Duke Math. J , vol.14 , pp. 877-887
    • Wolf, F.1


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