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

A. M. ManteroA. 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.

Macdonald formula for spherical functions on affine buildings

A. M. ManteroA. Zappa — 2011

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

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