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arXiv · 2110.00396

Quaternion Weyl Transform and some uniqueness results

Rupak Kumar Dalai·Somnath Ghosh·R. K. Srivastava
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Abstract

In this article, we study the boundedness and several properties of the quaternion Wigner transform. Using the quaternion Wigner transform as a tool, we define the quaternion Weyl transform (QWT) and prove that the QWT is compact for a certain class of symbols in $L^{r}\left(\mathbb{R}^{4}, \mathbb{Q}\right)$ with $1 \leq r \leq 2.$ Moreover, it can not be extended as a bounded operator for symbols in $L^{r}\left(\mathbb{R}^{4},\mathbb{Q}\right)$ for $2<r<\infty.$ In addition, we prove a rank analogue of the Benedicks-Amrein-Berthier theorem for the QWT. Further, we remark about the set of injectivity and Helgason's support theorem for the quaternion twisted spherical means.

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Rupak Kumar Dalai, Somnath Ghosh, R. K. Srivastava. 2021-10-01. Quaternion Weyl Transform and some uniqueness results. https://arxiv.org/abs/2110.00396

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