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Pré-Publication, Document De Travail Année : 2013

Functional properties of Hörmander's space of distributions having a specified wavefront set

Résumé

The space $D'_\Gamma$ of distributions having their wavefront sets in a closed cone $\Gamma$ has become important in physics because of its role in the formulation of quantum field theory in curved space time. In this paper, the topological and bornological properties of $D'_\Gamma$ and its dual $E'_\Lambda$ are investigated. It is found that $D'_\Gamma$ is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual $E'_\Lambda$ is a nuclear, barrelled and bornological normal space of distributions which, however, is not even sequentially complete. Concrete rules are given to determine whether a distribution belongs to $D'_\Gamma$, whether a sequence converges in $D'_\Gamma$ and whether a set of distributions is bounded in $D'_\Gamma$.
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Dates et versions

hal-00850192 , version 1 (05-08-2013)
hal-00850192 , version 2 (03-05-2014)

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Yoann Dabrowski, Christian Brouder. Functional properties of Hörmander's space of distributions having a specified wavefront set. 2013. ⟨hal-00850192v1⟩

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