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Eigenfunctions of the Laplace operators for buildings of type B ~ 2

A. M. Mantero, A. Zappa (2002)

Bollettino dell'Unione Matematica Italiana

We consider for an affine building of type B ~ 2 Helgason's conjecture with respect to Laplace operators defined over different types of vertices. We prove that there are cases in which the conjecture fails, since there exist eigenfunctions which are not the Poisson transform of finitely additive measures at the maximal boundary of the building.

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