We consider for an affine building of type B2 Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in whlch the conjecture fails, since there exist eigenfunctions which arenot the Poisson transform of finitely additive measures at the maximal boundary of the building.
Eigenfunctions of the Laplace operators for buildings of type B2
MANTERO, ANNA MARIA;ZAPPA, ANNA
2002-01-01
Abstract
We consider for an affine building of type B2 Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in whlch the conjecture fails, since there exist eigenfunctions which arenot the Poisson transform of finitely additive measures at the maximal boundary of the building.
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