Tauberian theorems for vector-valued Fourier and Laplace transforms

Chill, Ralph

Studia Mathematica, Tome 129 (1998), p. 55-69 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 1998-01-01

Zbl 0906.47006

EUDML-ID : urn:eudml:doc:216475

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