Abstract:We establish the condition (Ω) for smooth kernels of various types of convolution and differential operators. By the (DN )-(Ω) splitting theorem of Vogt and Wagner, this implies that these operators are surjective on the corresponding spaces of vector-valued smooth functions with values in a product of Montel (DF )-spaces whose strong duals satisfy the condition (DN ), e.g., the space D ′ (X) of distributions over an open set X ⊆ R d or the space S ′ (R d ) of tempered distributions. Most notably, we show that… Show more
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