Geodesic
Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}_2$
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 163-195

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider for an affine building of type $\tilde{B}_2$ 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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     author = {Mantero, A. M. and Zappa, A.},
     title = {Eigenfunctions of the {Laplace} operators for buildings of type $\tilde{B}_2$},
     journal = {Bollettino della Unione matematica italiana},
     pages = {163--195},
     publisher = {mathdoc},
     volume = {Ser. 8, 5B},
     number = {1},
     year = {2002},
     zbl = {1177.51010},
     mrnumber = {MR1881930},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a7/}
}
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Mantero, A. M.; Zappa, A. Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}_2$. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 163-195. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a7/