Beyond the plane-parallel approximation for redshift surveys
  Redshift space distortions privilege the location of the observer in
cosmological redshift surveys, breaking the translational symmetry of the
underlying theory. This violation of statistical homogeneity has consequences
for the modeling of clustering observables, leading to what are frequently
called `wide angle effects'. We study these effects analytically, computing
their signature in the clustering of the multipoles in configuration and
Fourier space. We take into account both physical wide angle contributions as
well as the terms generated by the galaxy selection function. Similar
considerations also affect the way power spectrum estimators are constructed.
We quantify, in an analytical way the biases which enter and clarify the
relation between what we measure and the underlying theoretical modeling. The
presence of an angular window function is also discussed. Motivated by this
analysis we present new estimators for the three dimensional Cartesian power
spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel
coefficients. We show how the latter have several interesting properties,
allowing in particular a clear separation between angular and radial modes.
