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- W2034663450 abstract "Motivated by the Schwartz space of tempered distributions $mathscr S^prime$ and the Kondratiev space of stochastic distributions $mathcal S_{-1}$ we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces $mathscr H_p^prime,pinmathbb N$, with decreasing norms $|cdot|_{p}$. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form $|f * g|_{p} leq A(p-q) |f|_{q}|g|_{p}$ for all $pge q+d$, where * denotes the convolution in the monoid, $A(p-q)$ is a strictly positive number and $d$ is a fixed natural number (in this case we obtain commutative topological $mathbb C$-algebras). Such an inequality holds in $mathcal S_{-1}$, but not in $mathscr S^prime$. We give an example of such a ring which contains $mathscr S^prime$. We characterize invertible elements in these rings and present applications to linear system theory" @default.
- W2034663450 created "2016-06-24" @default.
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- W2034663450 date "2011-06-28" @default.
- W2034663450 modified "2023-09-27" @default.
- W2034663450 title "New Topological C-Algebras with Applications in Linear Systems Theory" @default.
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