A note on bounded harmonic functions over homogeneous trees

• Autorzy: Gonzalez-Vieli F. J.
• Języki publikacji: EN

Abstrakty

EN

Let Τk be the homogeneous tree of degree k ≥ 3. J. M. Cohen and F. Colonna have proved that if ƒ is a bounded harmonic function on Τk, then [formula]for any adjacent vertices x and y in Τk. We give here a new and very simple proof of this inequality.

Słowa kluczowe

EN

bounded harmonic function; homogenous tree

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 4
• Strony: 697--700
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Gonzalez-Vieli F. J.

• Montoie 45 1007 Lausanne, Switzerland

Bibliografia

• [1] V. Anandam, Harmonic Functions and Potentials on Finite and Infinite Networks, Springer, Berlin, 2011.
• [2] N.L. Biggs, Discrete Mathematics, Clarendon Press, Oxford, 1985.
• [3] P. Cartier, Fonctions harmoniques sur un arbre, Sympos. Math. 9 (1972), 203–270.
• [4] J.M. Cohen, F. Colonna, The Bloch space of a homogeneous tree, Bol. Soc. Mat. Mex. 37 (1992), 63–82.
• [5] F.J. González Vieli, A two spheres problem on homogeneous trees, Combinatorica 18 (1998), 185–189.
• [6] E. Nelson, A proof of Liouville’s theorem, Proc. Amer. Math. Soc. 12 (1967), 995.