In mathematics, the double Fourier sphere (DFS) method is a simple 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.
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Introduction
First, a function
The function
where
The function
History
The DFS method was proposed by Merilees and developed further by Steven Orszag. The DFS method has been the subject of relatively few investigations since (a notable exception is Fornberg's work), 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 and to novel space-time spectral analysis.