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.

中文翻译：

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同构树上Laplacian弱L p-本征函数的刻画

在本文中，我们描述了齐次树上Laplacian的所有本征函数，它们是边界上定义的\（L ^ p \）函数的Poisson变换。使用对偶论证，我们还证明了齐次树上Helgason-Fourier变换的限制定理。