Positive definite functions on semi-homogeneous trees and spherical representations

Massimo A. Picardello

We consider the group $\mathrm{Aut}(T)$ of isometries of a semi-homogeneous tree $T=T_{q_{+},q_{-}}$ with valencies $q_{+}+1$ and $q_{-}+1$ and its two orbits $V_{+}$, $V_{-}$ respectively.…