Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 41
2008 発行

Parabolic Networks

Anandam Victor
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Description
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.