A LIMITATION OF THE KERNEL-METHOD FOR JOINT DISTRIBUTIONS OF ARBITRARY VARIABLES

Recently, Cohen has proposed a construction for joint distributions of arbitrary physical quantities, in direct generalization of joint time -frequency representations. Actually, this method encompasses two appr oaches: one based on operator correspondences and one based on weighti ng kernels. The literature has emphasized the kernel method due to its ease of analysis; however, its simplicity comes at a price. In this l etter, we use a simple example to demonstrate that the kernel method c annot generate all possible bilinear joint distributions. Our results suggest that the relationship between the operator method and the kern el method merits closer scrutiny.