Abstract
In this article, we characterize all eigenfunctions of the Laplacian on homogeneous trees, which are the Poisson transform of \(L^p\) functions defined on the boundary. Using the duality argument, we also proved the restriction theorem for the Helgason–Fourier transforms on a homogeneous tree.
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Second Author is supported by Institute fellowships of IIT Guwahati.
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Kumar, P., Rano, S.K. A characterization of weak Lp-eigenfunctions of the Laplacian on homogeneous trees. Annali di Matematica 200, 721–736 (2021). https://doi.org/10.1007/s10231-020-01011-3
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DOI: https://doi.org/10.1007/s10231-020-01011-3