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On absolutely representing systems in spaces of infinitely differentiable functions

100%

Korobeĭnik Y. F.

Studia Mathematica

2000

tom 139

nr 2

175-188

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 $ℝ^p$, p≥1, while K is a compact set in $ℝ^p$ with non-void interior K̇ such that $\overline K̇= K$. Moreover, absolutely representing systems of exponents in the space H(G) of functions analytic in an arbitrary domain $G ⊆ ℂ^p$ are also investigated.

Representing and absolutely representing systems

63%

Kadets V. M., Korobeĭnik Y. F.

Studia Mathematica

1992

tom 102

nr 3

217-223

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.

Ograniczanie wyników

2 Studia Mathematica

2 Korobeĭnik Y. F.

1 Kadets V. M.

1 2000

1 1992

Wyniki wyszukiwania

On absolutely representing systems in spaces of infinitely differentiable functions

Representing and absolutely representing systems