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Let Λ ⊂ Ω ⊂ ℝnbe open subsets. We construct a natural space 
of test functions on Λ such that the dual 
consists exactly of those distributions on Λ which can be extended to distributions on Ω. As an application of this representation we calculate the space 
of multiplication operators on as well as the space 
of absolutely regular extendable distributions.
Let 
be a linear partial differential operator with C∞- coefficients. The study of P(∂) as an operator in L2(ℝn) usually starts with the investigation of the minimal operator P0 which is the closure of P(∂) acting on 
. In the case of constant coefficients it is known that the domain D(P0) of P0 at least contains the space 
(cf. Schechter [4, p. 58, Lemma 1.2]).
