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arXiv · 2108.12729

Injectivity of spherical mean on Métivier Group

Rupak Kumar Dalai·R. K. Srivastava
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Abstract

In this article, we study the injectivity of the spherical mean for continuous functions on the Métivier group. The spherical mean is injective for $f(z, .)\in L^p(\mathbb{R}^m),~1\leq p \leq 2$ with tempered growth in $z$ variable. This result is also true for a class of functions in $L^p(\mathbb{C}^n),\,1\leq p\leq\infty$ without tempered growth. Further, we obtain a two-radii theorem for functions on the Métivier group, which are tempered in $z$ variable and periodic in the centre variable.

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Rupak Kumar Dalai, R. K. Srivastava. 2021-09-23. Injectivity of spherical mean on Métivier Group. https://arxiv.org/abs/2108.12729

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