Eigenfunctions of the Laplacian satisfying Hardy-type estimates on homogeneous trees

2023/11/01 by Sumit Kumar Rano, Rano, Sumit Kumar
Mathematics · #05C05 Secondary 39A12 #20E08 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary 43A85

paper · pdf · doi:10.48550/arxiv.2311.00623

openalex publication_date 2023/11/01 · openalex created_date 2023/11/03 · openalex updated_date 2026/07/28

Abstract

This work deals with the characterization of eigenfunctions of the Laplacian L on a homogeneous tree X, which satisfy certain growth conditions. More precisely, we shall prove that the Poisson transform on X provides an one-to-one correspondence between the subspace of all Hardy-type eigenfunctions of L on X and the Lebesgue spaces (possibly the set of all complex measures) on the boundary of X.

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