On the asymptotic behavior of the Wigner transform for large values of Planck’s constant

We give an asymptotic expression for the Wigner transform of certain functions for large values of Planck’s constant. We express our results with the help of Kazhdan constants depending on a compact set and a representation which are useful in the analysis of Kazhdan’s property T. This allows us to show that for every compact set there exist functions whose Wigner transform have no zeros thereon. We also determine such functions explicitly.