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Positive Eigenfunctions of the Laplacian and Conformal Densities on Homogeneous Trees
Author(s) -
Coornaert Michel,
Papadopoulos Athanase
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005164
Subject(s) - eigenfunction , homogeneous , laplace operator , conformal map , mathematics , harmonic function , tree (set theory) , pure mathematics , harmonic , mathematical analysis , eigenvalues and eigenvectors , combinatorics , physics , quantum mechanics
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 λ‐harmonic functions on the hyperbolic spaces H n and contained in the paper [ 9 ].