  Peculiar velocities induce apparent line of sight displacements of galaxies
in redshift space, distorting the pattern of clustering in the radial versus
transverse directions. On large scales, the amplitude of the distortion yields
a measure of the dimensionless linear growth rate $\beta \approx
\Omega^{0.6}/b$, where $\Omega$ is the cosmological density and $b$ the linear
bias factor. To make the maximum statistical use of the data in a wide angle
redshift survey, and for the greatest accuracy, the spherical character of the
distortion needs to be treated properly, rather than in the simpler plane
parallel approximation. In the linear regime, the redshift space correlation
function is described by a spherical distortion operator acting on the true
correlation function. It is pointed out here that there exists an operator,
which is essentially the logarithmic derivative with respect to pair
separation, which both commutes with the spherical distortion operator, and at
the same time defines a characteristic scale of separation. The correlation
function can be expanded in eigenfunctions of this operator, and these
eigenfunctions are eigenfunctions of the distortion operator. Ratios of the
observed amplitudes of the eigenfunctions yield measures of the linear growth
rate $\beta$ in a manner independent of the shape of the correlation function.
More generally, the logarithmic derivative $\partial/\partial\ln r$ with
respect to depth $r$, along with the square $L^2$ and component $L_z$ of the
angular momentum operator, form a complete set of commuting operators for the
spherical distortion operator acting on the density. The eigenfunctions of this
complete set of operators are spherical waves about the observer, with radial
part lying in logarithmic real or Fourier space.
