Behavior of biharmonic functions on Wiener's and Royden's compactifications
Y. K. Kwon, Leo Sario, Bertram Walsh · Annales de l’institut Fourier · 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 Δ Δ u = 0 ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.