Premium
A support theorem for quasianalytic functionals
Author(s) -
Heinrich Tobias,
Meise Reinhold
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410488
Subject(s) - mathematics , class (philosophy) , set (abstract data type) , function (biology) , pure mathematics , type (biology) , compact space , combinatorics , ecology , evolutionary biology , artificial intelligence , computer science , biology , programming language
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)