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Let      ϕ  \phi       be a central, noneven, positive type function on      SU ( 2 ) {\text {SU}}(2)       with      ϕ  ( e ) &gt; 1 \phi (e) &gt; 1      . For any polynomial function  p  on      SU ( 2 ) {\text {SU}}(2)      , let      V ( p ) V(p)       be the left convolution operator by      p / ( 1 −  ϕ  ) p/(1 - \phi )       on      L 2 ( SU ( 2 ) ) {L^2}({\text {SU}}(2))      , we prove that      V ( p ) / V ( 1 ) 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.

Théorème de Ney-Spitzer sur le dual de 𝑆𝑈(2)