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, ANNA MARIA;ZAPPA, ANNA
2009-01-01
Abstract
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 ∆.
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