18 citations · 34 across the 4 of their papers we have counts for
4 papers
A completeness-like relation for Bessel functions
Paulo H. F. Reimberg, L. Raul Abramo
Completeness relations are associated through Mercer's theorem to complete orthonormal basis of square integrable functions, and prescribe how a Dirac delta function can be decompo…
CMB and Random Flights: temperature and polarization in position space
Paulo H. F. Reimberg, L. Raul Abramo
The fluctuations in the temperature and polarization of the cosmic microwave background are described by a hierarchy of Boltzmann equations. In its integral form, this Boltzmann hi…
The Jacobi map for gravitational lensing: the role of the exponential map
Paulo H. F. Reimberg, L. Raul Abramo
We present a formal derivation of the key equations governing gravitational lensing in arbitrary space-times, starting from the basic properties of Jacobi fields and their expressi…
CMB in a box: causal structure and the Fourier-Bessel expansion
L. Raul Abramo, Paulo H. Reimberg, Henrique S. Xavier
This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wa…