2012/07/20 by E. Brüning, Erwin Brüning, Brüning, E. +3
Mathematics · Physics and Astronomy · #32A45 #32A70 #46F15 #Advanced Topology and Set Theory #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #math-ph #math.MP #msc:32A45 #msc:32A70 #msc:46F15
paper · pdf · doi:10.48550/arxiv.1207.4869
22 pages, 3 figures
arxiv created 2012/07/20 · openalex publication_date 2012/07/20 · arxiv updated 2012/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tempered ultra-hyperfunctions do not have the same type of localization properties as Schwartz distributions or Sato hyperfunctions; but the localization properties seem to play an important role in the proofs of the various versions of the edge of the wedge theorem. Thus, for tempered ultra hyper-functions, one finds a global form of this result in the literature, but no local version. In this paper we propose and prove a formulation of the edge of the wedge theorem for tempered ultra-hyperfunctions, both in global and local form. We explain our strategy first for the one variable case. We argue that in view of the cohomological definition of hyperfunctions and ultra-hyperfunctions, the global form of the edge of the wedge theorem is not surprising at all.