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Hudson's theorem for τ‐Wigner transforms

In this paper, after introducing a natural generalization of the classical Wigner transform, namely the τ‐Wigner transforms, depending on the parameter τ∈[0, 1], we study the problem of its positivity. In particular, we prove two theorems of Hudson‐type considering the action of the τ‐Wigner transforms on functions and on distributions, respectively. We give then an application of our results concerning Weyl and localization pseudo‐differential operators.