Unbounded Weyl transform on the Euclidean motion group and Heisenberg motion group

In this article, we define Weyl transform on second countable type - $I$ locally compact group $G,$ and as an operator on $L^2(G),$ we prove that the Weyl transform is compact when the symbol lies in $L^p(G\times \hat{G})$ with $1\leq p\leq 2.$ Further, for the Euclidean motion group and Heisenberg motion group, we prove that the Weyl transform can not be extended as a bounded operator for the symbol belongs to $L^p(G\times \hat{G})$ with $2

Keywords:

• Square-integrable function
• Second-countable space
• Type (model theory)
• Pure mathematics
• Locally compact group
• Mathematics
• Fourier transform
• Motion (geometry)
• Bounded operator
• Group (mathematics)

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