Functional Properties of Hörmander’s Space of Distributions Having a Specified Wavefront Set
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چکیده
The space D Γ of distributions having their wavefront sets in a closed cone Γ 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 Γ and its dual E ′ Λ are investigated. It is found that D Γ is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual E ′ Λ 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 Γ , whether a sequence converges in D Γ and whether a set of distributions is bounded in D Γ .
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تاریخ انتشار 2013