Abstract
We show that, if σ∈𝒮′(ℝ2d ) is a tempered distribution and, for some 1<p, q<∞, the Weyl operator L σ acts as a compact operator L σ:M p,q (ℝ d )→M p,q (ℝ d ), then the short time Fourier transform of σ vanishes at infinity. Some results on the eigenvalue distributions of the operators are included, as well as an example of a non-zero function with constant modulus, which is the symbol of a compact localization operator.
Acknowledgements
The research of the authors was partially supported by MEC and FEDER, Project MTM2004-02262 and net MTM2006-26627-E