A support theorem for quasianalytic functionals

For a weight function omega and an open set G in R-N denote by E-(omega) (G) (resp. epsilon({omega})(G)) the omega-ultradifferentiable functions of Beurling (resp. Roumieu) type on G. Using ideas of Hormander it is shown that the functionals u in epsilon((omega))' (G) and epsilon({omega})' (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 omega 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 is an element of epsilon({omega})' (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. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.