Effects of observer peculiar motion on the isotropic background
  frequency spectrum: from monopole to higher multipoles
  The observer peculiar motion produces boosting effects in the background
anisotropies with frequency spectral behaviours related to its spectrum. We
study how the frequency spectrum of the background isotropic monopole emission
is modified and transferred to the frequency spectra at higher multipoles, l.
We perform the analysis in terms of spherical harmonic expansion up to a
certain lmax, for various models from radio to far-IR. We derive a system of
linear equations to obtain spherical harmonic coefficients and provide explicit
solutions up to lmax=6 as linear combinations of the signals at N=lmax+1
colatitudes. The associated Legendre polynomials symmetry with respect to
{\pi}/2 is used to separate the system into two subsystems, one for l=0 and
even l, the other for odd l. This improves the solutions accuracy with respect
to an arbitrary colatitudes choice. We apply the method to analytical or
semi-analytical representions of monopole spectra, i.e. to four types of CMB
distortions, four types of extragalactic backgrounds superimposed to the CMB
Planckian spectrum and some combinations of them. We present our results in
terms of spherical harmonic coefficients, relationships between the observed
and intrinsic monopoles, maps, angular power spectra. We compare the method
results with the ones obtained using more computationally demanding numerical
integrations or map generation/inversion. The method is generalized to include
the effect of the observer motion relative to the Sun. Its simplicity and
efficiency can significantly alleviate the computational effort needed for
accurate predictions and for the analysis of future data. We discuss the
superposition of the CMB intrinsic anisotropies and of the effects induced by
the observer motion, exploring for the possibility of constraining the
intrinsic dipole embedded in the kinematic dipole, in the presence of CMB
spectral distortions.
