Multidimensional Tauberian Theorems for Vector-valued Distributions
نویسندگان
چکیده
We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform M φ(x, y) = (f ∗ φy)(x), (x, y) ∈ R n × R+, with kernel φy(t) = yφ(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quasiasymptotics in distribution spaces, and we give a necessary and sufficient condition for the existence of the trace of a distribution on {x0} × R. In addition, we present a new proof of Littlewood’s Tauberian theorem.
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