On the augmented density of a spherical anisotropic dynamic system
  This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that the partial derivatives of the Abel transformations of the augmented density must be non-negative. Applied for the separable augmented densities, this recovers the result of van Hese et al. (2011). 
J. An (NAOC)
math-ph astro-ph.CO astro-ph.GA math.MP