On the Bargmann Transform and the Wigner Transform

We observe that the Bargmann transform arises from the polardecomposition of a simple restriction operator. By virtue ofthe Bargmann transform, the Wigner transform is imbedded inthe geometric symmetry group of phase space. From this imbedding,we easily obtain that the spectrum of the Wigner transform consistsof {e^ik/12:k=0, 1, ..., 23}. 1991 Mathematics Subject Classification81R30, 47B38, 81S30.