Factorisation of analytic representations in the unit disk and   number-phase statistics of a quantum harmonic oscillator
  The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorisation and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorisation properties of a superposition state. 
A. Vourdas (University of Liverpool), C. Brif and A. Mann (Technion,   Haifa)