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arXiv · 1204.2773

Coxeter system of planes are sets of injectivity for the twisted spherical means on $\mathbb C^n$

R. K. Srivastava
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Abstract

In this article, we prove that any pair of perpendicular planes is a set of injectivity for the twisted spherical means (TSM) for $L^p(\mathbb C^n) (n\geq2)$ with $1\leq p\leq2.$ Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for $L^p(\mathbb C^n).$ We further observe that a set $S_R^{2n-1}\times\mathbb C$ is a set of injectivity for the TSM for a ceratin class of functions on $\mathbb C^{n+1}.$

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R. K. Srivastava. 2012-04-12. Coxeter system of planes are sets of injectivity for the twisted spherical means on $\mathbb C^n$. https://arxiv.org/abs/1204.2773

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