Tauberian class estimates for vector-valued distributions
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 $M^{\mathbf{f}}_φ(x,y)=(\mathbf{f}\astφ_{y})(x)$, where the kernel $φ$ is a test function and $φ_{y}(\cdot)=y^{-n}φ(\cdot/y)$. We investigate conditions which ensure that a distribution that a priori takes values in locally convex space actually takes values in a …