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

2011/03/23 by R. K. Srivastava, Srivastava, R. K. · 1 citation
Mathematics · #43A85 (Primary) #44A35 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A85 #msc:44A35

paper · pdf · doi:10.48550/arxiv.1103.4571

This article is accepted in J. Funct. Anal. jointly with arXiv:1204.2773

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

Abstract

It is well known that a line in \mathbb R² is not a set of injectivity for the spherical means for odd functions about that line. We prove that any line passing through the origin is a set of injectivity for the twisted spherical means (TSM) for functions f∈ L²(\mathbb C), whose each of spectral projection e^(1)/(4)|z|2f×φ_k is a polynomial. Then, we prove that any Coxeter system of even number of lines is a set of injectivity for the TSM for L^q(\mathbb C),~1≤ q≤2.

Citations

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

Cited by

• Sets of injectivity for weighted twisted spherical means and support theorems
• Coxeter system of planes are sets of injectivity for the twisted spherical means on \mathbb Cⁿ

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