Moment operators of the Cartesian margins of the phase space observables
  The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position operator and those of the $y$-margin are polynomials of the momentum operator. 
J. Kiukas, P. Lahti, K. Ylinen