In mathematics, the double Fourier sphere (DFS) method is a technique that transforms a function defined on the surface of the sphere to a function defined on a rectangular domain while preserving periodicity in both the longitude and latitude directions.
on the sphere is written as
f ( λ , θ )
using spherical coordinates, i.e., The function
f ( λ , θ )
The periodicity in the latitude direction has been lost.
To recover it, the function is "doubled up” and a related function on
g ( λ , θ ) = f ( λ − π , θ )
can be expanded into a double Fourier series The DFS method was proposed by Merilees[1] and developed further by Steven Orszag.
[2] The DFS method has been the subject of relatively few investigations since (a notable exception is Fornberg's work),[3] perhaps due to the dominance of spherical harmonics expansions.
Over the last fifteen years it has begun to be used for the computation of gravitational fields near black holes[4] and to novel space-time spectral analysis.
This black hole-related article is a stub.