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The space \(\dot{\mathcal {B}}'\) of distributions vanishing at infinity: duals of tensor products

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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 dual of \(E \widehat{\otimes }F\) if E and F are quasi-complete and F is not necessarily semi-reflexive.

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Authors and Affiliations

  1. Wolfgang Pauli Institut, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    E. A. Nigsch

  2. Institut für Mathematik, Universität Innsbruck, Technikerstraße 13, 6020, Innsbruck, Austria

    N. Ortner

Authors
  1. E. A. Nigsch
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  2. N. Ortner
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Correspondence to E. A. Nigsch.

Additional information

E. A. Nigsch was supported by the Austrian Science Fund (FWF) Grants P23714 and P26859.

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Nigsch, E.A., Ortner, N. The space \(\dot{\mathcal {B}}'\) of distributions vanishing at infinity: duals of tensor products. RACSAM 112, 251–269 (2018). https://doi.org/10.1007/s13398-016-0371-6

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  • DOI: https://doi.org/10.1007/s13398-016-0371-6

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