Premium
Hudson's theorem for τ‐Wigner transforms
Author(s) -
Boggiatto P.,
De Donno G.,
Oliaro A.
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt038
Subject(s) - mathematics , generalization , wigner distribution function , action (physics) , type (biology) , pure mathematics , mathematical analysis , quantum mechanics , quantum , ecology , physics , biology
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.