Théorème de Ney-Spitzer sur le dual de ${\rm SU}(2)$

Let $\phi$ be a central, noneven, positive type function on ${\text{SU}}(2)$ with $\phi (e) < 1$. For any polynomial function p on ${\text{SU}}(2)$, let $V(p)$ be the left convolution operator by $p/(1 - \phi )$ on ${L^2}({\text{SU}}(2))$, we prove that $V(p)/V(1)$ is a pseudodifferential operator of order 0 and give an explicit formula for its principal symbol. This is interpreted in terms of Martin compactification of a quantum random walk.