Spherical means on Métivier groups and support theorem

2021/08/26 by Rupak Kumar Dalai, Dalai, Rupak Kumar, Somnath Ghosh +4 · 1 citation
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.2108.11744

18 pages

arxiv created 2021/08/26 · openalex publication_date 2021/08/26 · arxiv updated 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Z_{r, R} be the space of continuous functions on the annulus B_{r, R} in \mathbb Cⁿ whose λ-twisted spherical mean, in the set up of the Métivier group, vanishes over the spheres S_s(z)⊂ B_{r, R} with ball B_r(0)⊆ B_s(z). We characterize the spherical harmonic coefficients of functions in Z_{r, R}, eventually, in terms of polynomial growth, by which we infer support theorem. Further, we prove that non-harmonic complex cone and the boundary of a bounded domain are sets of injectivity for the λ-twisted spherical means.

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