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Behavior of biharmonic functions on Wiener's and Royden's compactifications

Y. K. Kwon; Leo Sario; Bertram Walsh — 1971

Annales de l'institut Fourier

Let $R$ be a smooth Riemannian manifold of finite volume, $Δ$ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of $R$ are found, and for biharmonic functions (those for which $Δ Δ u = 0$ ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.

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