Sets of injectivity for weighted twisted spherical means and support theorems

2010/12/23 by R. K. Srivastava, Srivastava, R. K.
Mathematics · Physics and Astronomy · #43A85 (Primary) 44A35 (Secondary) #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.FA #math.MP #msc:43A85 #msc:44A35

paper · pdf · doi:10.48550/arxiv.1012.5167

Published: J. Fourier Anal. Appl., 18(2012), no. 3, 592-608. arXiv admin note: text overlap with arXiv:1103.4571

openalex publication_date 2010/12/23 · arxiv created 2012/05/17 · arxiv updated 2012/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that the spheres S_R(o)=\z∈\mathbb Cⁿ: |z|=R\ are sets of injectivity for the weighted twisted spherical means (WTSM) for a suitable class of functions on \mathbb Cⁿ. The weights here are spherical harmonics on S^2n-1. In general, the question of set of injectivity for the twisted spherical means (TSM) with real analytic weight is still open. We would like to refer to \citeNRR, for some results on the sets of injectivity for the spherical means with real analytic weights in the Euclidean setup.

Citations

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

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