2013/08/05 by Yoann Dabrowski, Dabrowski, Yoann, Christian Brouder +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topology and Set Theory #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #advanced mathematical theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1308.1061
38 pages, no figure. Nuclearity and further functional properties are added in this second version
openalex publication_date 2013/08/05 · arxiv created 2014/05/04 · arxiv updated 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.