On the Weinstein-Wigner transform and Weinstein-Weyl transform

摘要

In this paper, we define and study the Weinstein-Wigner transform and we prove its inversion formula. Next, we introduce and study the Weinstein-Weyl transform W sigma with symbol sigma and we give an integral relation between it and the Weinstein-Wigner transform. At last, we give criteria in terms of sigma for boundedness and compactness of the transform W sigma.