Turkish Journal of Mathematics
DOI

Abstract
Let Q be a compactum in~\mathbb{R}^p, p\geqslant1, such that int Q\neq\varnothing and Q=\overline{ int Q}. Denote by C^{\infty}[Q] the space of functions from C^{\infty}( int Q) uniformly continuous in int Q together with all their partial derivatives. The conditions of the existence of absolutely representing systems of exponentials with purely imaginary exponents in the space C^{\infty}[Q] and some of its subspaces of DenjoyCarleman type are investigated. It is also proved under rather general assumptions that there is no such absolutely representing systems in the space E(G)=\operatornamewithlimits{proj}\limits_ {\overleftarrow {Q\in \mathcal{F}_G}}E[Q] where G is an arbitrary open set in~\mathbb{R}^p, E[Q] is C^{\infty}[Q] or its subspace mentioned above and \mathcal{F}_G is the totality of all nonempty compact sets \mathcal{K} in G with the property \mathcal{K}= \overline{ int \mathcal{K}}.
First Page
503
Last Page
518
Recommended Citation
KOROBEINIK, YU. F. (2001) "Absolutely Representing Systems of Exponentials in the Spaces of InfinitelyDifferentiable Functions and Extendability in the Sense of Whitney," Turkish Journal of Mathematics: Vol. 25: No. 4, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol25/iss4/5