Parabolic Networks

抄録・要旨

In an infinite network N without positive potentials (called a parabolic network), a generalized version of the Dirichlet problem is solved in an arbitrary subset of N. This solution is shown to play a pivotal role in the potential-theoretic study in N, such as the construction of an analogue of the logarithmic potential in N, balayage, harmonic and superharmonic extension condenser principle etc.