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On absolutely representing systems in spaces of infinitely differentiable functions

Yu. Korobeĭnik — 2000

Studia Mathematica

The main part of the paper is devoted to the problem of the existence of absolutely representing systems of exponentials with imaginary exponents in the spaces C ( G ) and C ( K ) of infinitely differentiable functions where G is an arbitrary domain in p , p≥1, while K is a compact set in p with non-void interior K̇ such that K ¯ ̇ = K . Moreover, absolutely representing systems of exponents in the space H(G) of functions analytic in an arbitrary domain G p are also investigated.

Representing and absolutely representing systems

V. KadetsYu. Korobeĭnik — 1992

Studia Mathematica

We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.

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