Coxeter system of planes are sets of injectivity for the twisted spherical means on \mathbb Cⁿ

2012/04/12 by R. K. Srivastava, Srivastava, R. K. · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1204.2773

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

arxiv created 2014/03/14 · arxiv updated 2014/03/17

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 Cⁿ) (n≥2) with 1≤ p≤2. Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for L^p(\mathbb Cⁿ). We further observe that a set S_R^2n-1×\mathbb C is a set of injectivity for the TSM for a ceratin class of functions on \mathbb Cⁿ⁺¹.

Citations

• Coxeter system of lines are sets of injectivity for the twisted spherical means on \mathbb C

Cited by

• Non-harmonic cones are sets of injectivity for the twisted spherical means on \mathbb Cⁿ
• Coxeter system of lines are sets of injectivity for the twisted spherical means on \mathbb C

Related

• Coxeter system of lines are sets of injectivity for the twisted spherical means on \mathbb C
• Sets of injectivity for weighted twisted spherical means and support theorems
• Non-harmonic cones are sets of injectivity for the twisted spherical means on \mathbb Cⁿ
• Spherical means on Métivier groups and support theorem
• The combinatorics of twisted involutions in Coxeter groups