Fredholm methods for billiard eigenfunctions in the coherent state   representation
  We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium eigenfunctions, which is written in terms of classical invariants: periodic points, their monodromy matrices and Maslov indices. 
Fernando P. Simonotti and Marcos Saraceno