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arXiv · 1604.02846

The space $\dot{\mathcal{B}}'$ of distributions vanishing at infinity - duals of tensor products

Eduard A. Nigsch·Norbert Ortner
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Abstract

Analogous to L.~Schwartz' study of the space $\mathcal{D}'(\mathcal{E})$ of semi-regular distributions we investigate the topological properties of the space $\mathcal{D}'(\dot{\mathcal{B}})$ of semi-regular vanishing distributions and give representations of its dual and of the scalar product with this dual. In order to determine the dual of the space of semi-regular vanishing distributions we generalize and modify a result of A. Grothendieck on the duals of $E \hat\otimes F$ if $E$ and $F$ are quasi-complete and $F$ is not necessarily semi-reflexive.

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Eduard A. Nigsch, Norbert Ortner. 2016-04-11. The space $\dot{\mathcal{B}}'$ of distributions vanishing at infinity - duals of tensor products. https://arxiv.org/abs/1604.02846

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