A new approach to the star-genvalue equation
  We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyl-type representation of the star-product and of the properties of the cross-Wigner transform, which appears as an intertwining operator. 
M. de Gosson, Franz Luef