Tauberian theorems for vector-valued Fourier and Laplace transforms

Ralph Chill

Studia Mathematica (1998)

  • Volume: 128, Issue: 1, page 55-69
  • ISSN: 0039-3223

Abstract

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

How to cite

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Chill, Ralph. "Tauberian theorems for vector-valued Fourier and Laplace transforms." Studia Mathematica 128.1 (1998): 55-69. <http://eudml.org/doc/216475>.

@article{Chill1998,
abstract = {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.},
author = {Chill, Ralph},
journal = {Studia Mathematica},
keywords = {Tauberian theorem; Fourier transform; Laplace transform; asymptotically almost periodic; analytic Radon-Nikodym property; Cauchy problem; distributional Fourier transform; Tauberian theorems; Fourier and Laplace transforms; analytic Radon-Nikodým property},
language = {eng},
number = {1},
pages = {55-69},
title = {Tauberian theorems for vector-valued Fourier and Laplace transforms},
url = {http://eudml.org/doc/216475},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Chill, Ralph
TI - Tauberian theorems for vector-valued Fourier and Laplace transforms
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 1
SP - 55
EP - 69
AB - 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.
LA - eng
KW - Tauberian theorem; Fourier transform; Laplace transform; asymptotically almost periodic; analytic Radon-Nikodym property; Cauchy problem; distributional Fourier transform; Tauberian theorems; Fourier and Laplace transforms; analytic Radon-Nikodým property
UR - http://eudml.org/doc/216475
ER -

References

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