Starting from a complete family for the unit sphere Sn in the complex n-space Cn (whose elements are coherent states attached to the Barut–Girardello space), we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation of the asymptotic behaviour of functions in the complete family. Furthermore, in an analogous manner (slightly weaker) we obtain the asymptotic expansion of the covariant symbol of a pseudo-differential operator on L2(Sn).

中文翻译：

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Cn单位球上的相干态及其相关协变符号的渐近展开

从复数n空间Cn中的单位球面Sn的一个完整族（其元素是与Barut-Girardello空间相连的相干状态）开始，我们获得了相关Berezin变换的渐近展开。证明涉及整个家族中函数渐近行为的计算。此外，以类似的方式（稍弱），我们获得L2（Sn）上伪微分算符的协变符号的渐近展开。