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

R. K. Srivastava

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

Functional Analysis 2014-03-17 v4

Authors: R. K. Srivastava

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 $\mathbb C^{n+1}.$

Keywords

twisted spherical means sets of injectivity Coxeter system of planes perpendicular planes $L^p(\mathbb C^n)$

Cite

@article{arxiv.1204.2773,
  title  = {Coxeter system of planes are sets of injectivity for the twisted spherical means on $\mathbb C^n$},
  author = {R. K. Srivastava},
  journal= {arXiv preprint arXiv:1204.2773},
  year   = {2014}
}

Comments

This article is accepted in J. Funct. Anal. jointly with arXiv:1103.4571

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

Abstract

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