Let ∆ be a thick affine building of type ~G_2 . We prove that any eigenfunction of the Laplace operators of ∆, associated with a pair (γ_1 , γ_2 ), is the Poisson transform of a suitable finitely additive measure on the maximal boundary Ω of ∆, by using only the combinatorial structure of ∆.
Eigenfunctions of the Laplace Operators for a building of type G_2 / MANTERO A. M; ZAPPA A.. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - STAMPA. - (9) 2(2009), pp. 483-508.