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

Let $R$ be a smooth Riemannian manifold of finite volume, $\Delta $ 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 $\Delta \Delta u=0$) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.