Decomposition, representation and extension of the harmonic functions. (English) Zbl 0662.31008
Using the probabilistic method, we obtain a decomposition theorem for the harmonic functions, generalized and strengthened some theorems: Doob’s theorem on the limit behaviors of the superharmonic functions, Bocher’s theorem on the representation of the harmonic functions and the extension theorem of the harmonic functions etc.
MSC:
31C05 | Harmonic, subharmonic, superharmonic functions on other spaces |