- Tytuł:
- Tauberian theorems for vector-valued Fourier and Laplace transforms
- Autorzy:
- Chill, Ralph
- Powiązania:
- https://bibliotekanauki.pl/articles/1218589.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Tauberian theorem
Fourier transform
Laplace transform
asymptotically almost periodic
analytic Radon-Nikodym property
Cauchy problem - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1998, 128, 1; 55-69
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł