Injectivity of spherical mean on Métivier Group

2021/08/29 by Rupak Kumar Dalai, Dalai, Rupak Kumar, Rajula Srivastava +2
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA

paper · pdf · doi:10.48550/arxiv.2108.12729

updated, 13 pages

openalex publication_date 2021/08/29 · arxiv created 2021/09/23 · arxiv updated 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the injectivity of the spherical mean for continuous functions on the Métivier group. The spherical mean is injective for f(z, .)∈ L^p(ℝ^m),~1≤ p ≤ 2 with tempered growth in z variable. This result is also true for a class of functions in L^p(ℂⁿ), 1≤ p≤∞ without tempered growth. Further, we obtain a two-radii theorem for functions on the Métivier group, which are tempered in z variable and periodic in the centre variable.

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