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1998 | 128 | 1 | 55-69
Tytuł artykułu

Tauberian theorems for vector-valued Fourier and Laplace transforms

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Języki publikacji
EN
Abstrakty
EN
Let X be a Banach space and $f ∈ L^1_loc(ℝ;X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
Czasopismo
Rocznik
Tom
128
Numer
1
Strony
55-69
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-03-13
poprawiono
1997-08-21
Twórcy
autor
Bibliografia
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  • [2] W. Arendt and C. J. K. Batty, Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half line, J. London Math. Soc., to appear.
  • [3] W. Arendt and C. J. K. Batty, Almost periodic solutions of first and second order Cauchy problems, J. Differential Equations 137 (1997), 363-383.
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  • [5] C. J. K. Batty, J. M. A. M. van Neerven and F. Räbiger, Local spectra and individual stability of uniformly bounded $C_0$-semigroups, Trans. Amer. Math. Soc., to appear.
  • [6] C. J. K. Batty, J. M. A. M. van Neerven and F. Räbiger, Tauberian theorems and stability of solutions of the Cauchy problem, ibid., to appear.
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  • [21] J. M. A. M. van Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, Oper. Theory Adv. Appl. 88, Birkhäuser, 1996.
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Bibliografia
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