Tauberian theorems for vector-valued Fourier and Laplace transforms

• Autorzy: Ralph Chill
• 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.

Słowa kluczowe

EN

Tauberian theorem; Fourier transform; Laplace transform; asymptotically almost periodic; analytic Radon-Nikodym property; Cauchy problem

Kategorie tematyczne

• 44A10: Laplace transform
• 47A35: Ergodic theory
• 34C28: Complex behavior, chaotic systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 1
• Strony: 55-69

Daty

wydano

1998

otrzymano

1997-03-13

poprawiono

1997-08-21

Twórcy

autor

Ralph Chill

• Abteilung Mathematik V, Universität Ulm, 89069 Ulm, Germany

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