A Characterization of the Locally Finite Networks Admitting Non-Constant Harmonic Functions of Finite Energy

Author:

Carmesin Johannes

Publisher

Springer Science and Business Media LLC

Subject

Analysis

Reference11 articles.

1. Biggs, N.L.: Algebraic potential theory on graphs. Bull. Lond. Math. Soc. 29, 641–682 (1997)

2. Carmesin, J.: Harmonic functions of finite ℓ p -norm in infinite networks (2011, in preparation)

3. Diestel, R.: Graph Theory, 3rd edn. Springer, Berlin (2005). Electronic edition available at: http://www.math.uni-hamburg.de/home/diestel/books/graph.theory

4. Georgakopoulos, A.: Uniqueness of electrical currents in a network of finite total resistance. J. Lond. Math. Soc. 82(1), 256–272 (2010). doi: 10.1112/jlms/jdq034

5. Lyons, R., Peres, Y.: Probability on Trees and Networks. Cambridge University Press, Cambridge (2011, in preparation). Current version available at http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html

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