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Journal of the London Mathematical Society 1997 55(3):609-624; doi:10.1112/S0024610797005164
© 1997 by London Mathematical Society
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© The London Mathematical Society

Positive Eigenfunctions of the Laplacian and Conformal Densities on Homogeneous Trees

Michel Coornaert and Athanase Papadopoulos

Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS 7 rue René Descartes, 67084 Strasbourg Cedex, France

Received 14 February 1995. Revision received 11 May 1995.

In this paper, we study some asymptotic aspects of the positive eigenfunctions of the combinatorial Laplacian associated to a homogeneous tree. The results are inspired by results of Dennis Sullivan concerning {lambda}-harmonic functions on the hyperbolic spaces Hn and contained in the paper [9].


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