Behavior of Biharmonic Functions on Wiener's and Royden's Compactifications - Kwon, Young Koan (Institutional Knowledge at Singapore Management University, 1971)
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 ΔΔu=0) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.