On the Bargmann Transform and the Wigner Transform

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Abstract

We observe that the Bargmann transform arises from the polar decomposition of a simple restriction operator. By virtue of the Bargmann transform, the Wigner transform is imbedded in the geometric symmetry group of phase space. From this imbedding, we easily obtain that the spectrum of the Wigner transform consists of {eikπ/12:k=0, 1, …, 23}. 1991 Mathematics Subject Classification 81R30, 47B38, 81S30.