Geodesic
Tauberian theorems for vector-valued Fourier and Laplace transforms
Studia Mathematica, Tome 128 (1998) no. 1, pp. 55-69 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm-128-1-55-69
Keywords: Tauberian theorem, Fourier transform, Laplace transform, asymptotically almost periodic, analytic Radon-Nikodym property, Cauchy problem 
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Ralph Chill. Tauberian theorems for vector-valued Fourier and Laplace transforms. Studia Mathematica, Tome 128 (1998) no. 1, pp. 55-69. doi: 10.4064/sm-128-1-55-69

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