A Paley-Wiener type theorem for a weighted space of infinitely differentiable functions (Q2759289)
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scientific article; zbMATH DE number 1681694
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Paley-Wiener type theorem for a weighted space of infinitely differentiable functions |
scientific article; zbMATH DE number 1681694 |
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A Paley-Wiener type theorem for a weighted space of infinitely differentiable functions (English)
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3 January 2002
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Paley-Wiener type theorem
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Young transform
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weighted space
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The author studies the relation between a certain weighted space \(G\) of infinitely differentiable functions on the real line and a certain weighted space \(P\) of entire functions on the complex plane. His main result says that the Fourier-Laplace transform is a topological isomorphism from the strong dual \(G^*\) of \(G\) onto \(P\). Along the way, he shows that the polynomials are dense in \(G\). His rather technical analytic apparatus uses a result of \textit{M. I. Solomeshch} [VINITI 1992, Dep. 2447-B92 (Russian), Inst. Mat. Ural. Otdel. Ross. Akad. Nauk UFA (1992)].
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