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- W2005821710 abstract "Abstract For a Lie group G , we show that the map taking a pair of test functions to their convolution, is continuous if and only if G is σ-compact. More generally, consider with t ≤ r + s , locally convex spaces E 1 , E 2 and a continuous bilinear map b : E 1 × E 2 → F to a complete locally convex space F . Let be the associated convolution map. The main result is a characterization of those ( G ; r ; s ; t ; b ) for which β is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed as well as convolution of compactly supported L 1 -functions and convolution of compactly supported Radon measures." @default.
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- W2005821710 date "2014-02-01" @default.
- W2005821710 modified "2023-10-03" @default.
- W2005821710 title "Continuity of Convolution of Test Functions on Lie Groups" @default.
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- W2005821710 doi "https://doi.org/10.4153/cjm-2012-035-6" @default.
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