A support theorem for quasianalytic functionals

✍ Scribed by Tobias Heinrich; Reinhold Meise

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 306 KB
• Volume: 280
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410488

✦ Synopsis

Abstract

For a weight function ω and an open set G in ℝ^N^ denote by ℰ(ω)(G) (resp. E~{ω }~(G)) the ω ‐ultradifferentiable functions of Beurling (resp. Roumieu) type on G. Using ideas of Hörmander it is shown that the functionals u in ℰ′(ω)(G) and ℰ′~{ω }~(G) can be embedded into the realanalytic functionals on ℝ^N^ and that there is a smallest supporting set for u in the corresponding class which coincides with the realanalytic (hyperfunction) support of u. Moreover, if ω is quasianalytic and if a compact subset K of G is the union of the compact sets K~1~ and K~2~ then each u ∈ ℰ′~{ω }~(G) which is supported by K can be decomposed as u = u~1~ + u~2~, where u~j~ is supported by K~j~ for j = 1, 2. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)