2014/11/11 by Yoann Dabrowski, Dabrowski, Yoann
Mathematics · Physics and Astronomy · #46F12 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Primary 46F05 #Secondary : 81T20 #math.FA #msc:46F05 #msc:46F12 #msc:81T20
paper · pdf · doi:10.48550/arxiv.1411.3012
59 pages
arxiv created 2014/11/11 · openalex publication_date 2014/11/11 · arxiv updated 2014/11/13 · openalex created_date 2022/09/03 · openalex updated_date 2026/08/04
The space D'Λ of distributions having their C^∞ wavefront set in a cone Λ has become important in physics because of its role in the formulation of quantum field theory in curved spacetime. It is also a basic object in microlocal analysis, but not well studied from a functional analytic viewpoint. In order to compute its completion in the open cone case, we introduce generalized spaces D'γ,Λ where we also control the union of Hs-wave front sets in a second cone γ contained in Λ. We can compute bornological and topological duals, completions and bornologifications of natural topologies for spaces in this class. All our topologies are nuclear, ultrabornological when bornological and we can describe when they are quasi-LB. We also give concrete microlocal representations of bounded and equicontinuous sets in those spaces and work with general support conditions including future compact or space compact support conditions on globally hyperbolic manifolds, as motivated by physics applications to be developed in a second paper.