Eigenfunctions of the Laplace operators for buildings of type B~2
Mantero, A. M. ; Zappa, A.
Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 163-195 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Si considera per un palazzo affine di tipo B~2 la congettura di Helgason relativa a operatori di Laplace definiti su diversi tipi di vertici. Si prova che ci sono casi in cui la congettura non è verificata, in quanto esistono autofunzioni che non sono la trasformata di Poisson di misure finitamente additive sulla frontiera massimale del palazzo

Publié le : 2002-02-01
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     author = {A. M. Mantero and A. Zappa},
     title = {Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}\_2$},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {163-195},
     zbl = {1177.51010},
     mrnumber = {1881930},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_1_163_0}
}

Mantero, A. M.; Zappa, A. Eigenfunctions of the Laplace operators for buildings of type $\tilde{B}_2$. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 163-195. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_1_163_0/

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