CONDITIONS FOR THE CONVOLUTION OF 2 WIGNER DISTRIBUTIONS TO BE ITSELF A WIGNER DISTRIBUTION
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abstract
The convolution of two Wigner distribution functions (WDF's) is always non-negative, but not always a WDF, as Jagannathan et al. [Phys. Lett. A 120, 161 (1987)] have shown. In this paper conditions are given that are sufficient, and probably necessary, for such a convolution to be a WDF, and a new characterization of Gaussian WDF's is obtained as a by-product. 1988 American Institute of Physics.
