Preprint Series 2017

2017:02
K. Ivanov and
P. Petrushev
The purpose of this article is to construct highly localized summability kernels on the unit sphere in ${\bf R}^d$ that are restrictions to the sphere of linear combinations of a small number of shifts of the fundamental solution of the Laplace equation (Newtonian kernel) with poles outside the unit ...
[Full Abstract] 
2017:01
K. Ivanov,
N. Pavlis, and
P. Petrushev
Gravimetric quantities are commonly represented in terms of high degree surface or solid spherical harmonics. After EGM2008, such expansions routinely extend to spherical harmonic degree 2190, which makes the computation of gravimetric quantities at a large number of arbitrarily scattered points in space using harmonic synthesis, a very computationally demanding ...
[Full Abstract]