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The space ú Bof distributions vanishing at infinity - duals of tensor products

Analogous to L. Schwartz’ study of the space D ′ (E) of semi-regular distributions we investigate the topological properties of the space D ′ ( u 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 Eb ⊗F if E and F are quasi-complete and F is not necessarily semireflexive.