Abstract
In this article, distributions with values in a (not necessarily locally convex) topological vector space E are defined to be the elements of
. Operations on such distributions can be introduced as usual. In general, not every continuous E-valued function defines a distribution, but the elements of
do. A large part of the theory is reduced to the locally convex case by use of the so-called locally convex subspaces of E (cf. [2]). We prove that the presheaf of E-valued distributions on open subsets of ℝN is a topological sheaf. We give integral representation theorems for bounded mappings in
and
, and we show that, on bounded subsets ω of ℝN, each distribution defined on ℝN with values in a (p)-space is a derivative of a function in
.
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Während der Fertigstellung eines Teils dieser Arbeit Research Associate der University of Maryland, Md. 20742, USA.
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Bierstedt, KD., Meise, R. Distributionen mit Werten in topologischen Vektorräumen I. Manuscripta Math 10, 35–63 (1973). https://doi.org/10.1007/BF01677007
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DOI: https://doi.org/10.1007/BF01677007