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Published online by Cambridge University Press: 24 October 2008
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.