New topological \(\mathbb C\)-algebras with applications in linear systems theory (Q2909260)
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scientific article; zbMATH DE number 6074045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New topological \(\mathbb C\)-algebras with applications in linear systems theory |
scientific article; zbMATH DE number 6074045 |
Statements
30 August 2012
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nuclear spaces
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topological rings
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Wick product
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convolution
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white noise space
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Våge inequality
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Schwartz space of tempered distributions
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Kondratiev spaces
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linear systems on commutative rings
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New topological \(\mathbb C\)-algebras with applications in linear systems theory (English)
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The authors define a wide family of nuclear topological vector spaces, as dual of certain Fréchet spaces. This family includes the Schwartz space of tempered distributions \(\mathcal S'\) and the Kondratiev space of stochastic distributions \(S_{-1}\), and is closed under tensor products. In particular, the authors show that these spaces are topological \(\mathbb C\)-algebras and give a characterization of their invertible elements. They also present some applications to linear system theory.
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