Displaying similar documents to “A relation between Fourier and Mellin averages”

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada, Jasson Vindas (2013)

Czechoslovak Mathematical Journal

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We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows...

Tauberian theorems for vector-valued Fourier and Laplace transforms

Ralph Chill (1998)

Studia Mathematica

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Let X be a Banach space and f ∈ L l 1 o c ( 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.