Analysis of L^p-type estimates of Poisson transform on Homogeneous Trees

2018/08/29 by Pratyoosh Kumar, Kumar, Pratyoosh, Sumit Kumar Rano +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1808.09659

openalex publication_date 2018/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove the restriction theorem for Helgason-Fourier transform on homogeneous tree. Our proof is based on the duality argument and the norm estimates of Poisson transform. We also characterize all eigenfunctions of the laplacian on homogeneous tree which are Poisson transform of L^p functions defined on the boundary.

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