78 research outputs found
Tauberian class estimates for vector-valued distributions
We study Tauberian properties of regularizing transforms of vector-valued
tempered distributions, that is, transforms of the form
, where the
kernel is a test function and
. We investigate conditions which
ensure that a distribution that a priori takes values in locally convex space
actually takes values in a narrower Banach space. Our goal is to characterize
spaces of Banach space valued tempered distributions in terms of so-called
class estimates for the transform . Our results
generalize and improve earlier Tauberian theorems of Drozhzhinov and Zav'yalov
[Sb. Math. 194 (2003), 1599-1646]. Special attention is paid to find the
optimal class of kernels for which these Tauberian results hold.Comment: 24 pages. arXiv admin note: substantial text overlap with
arXiv:1012.509
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