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Transactions of the American Mathematical Society

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

Author: Philippe Biane
Journal: Trans. Amer. Math. Soc. 345 (1994), 179-194
MSC: Primary 60J50; Secondary 22E99, 47G30, 60B15, 81S25
MathSciNet review: 1225572
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Abstract: 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.

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