An integral representation and fine limits at infinity for functions whose Laplacians iterated \(m\) times are measures (Q1378303)

The author studies the behaviour at infinity of functions \(u\) on \(\mathbb{R}^n\) for which \(\Delta^mu \geq 0\) in the weak sense. To realise this aim he considers on one hand, the conditions for polyharmonic functions to be polynomials and, on the other hand, he establishes an integeral representation for \(u\) as a generalisation of Riesz's decomposition theorem for superharmonic functions. So, the main results of the paper are contained in three theorems. The study is a generalisation of investigations by the author in other papers published since 1983. Moreover, some particular results are compared with results of other authors using different methods.