Approximation properties of the double Fourier sphere method
arXiv:2108.05662 · doi:10.1007/s00041-022-09928-4
Abstract
We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a function defined on the two-dimensional torus. Then the resulting function can be written as a Fourier series yielding an approximation of the original function. We show that the DFS method preserves smoothness: it continuously maps spherical Hölder spaces into the respective spaces on the torus, but it does not preserve spherical Sobolev spaces in the same manner. Furthermore, we prove sufficient conditions for the absolute convergence of the resulting series expansion on the sphere as well as results on the speed of convergence.
References in corpus (7)
- Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
- The Funk-Radon transform for hyperplane sections through a common point
- A Combination of Downward Continuation and Local Approximation for Harmonic Potentials
- An SVD in Spherical Surface Wave Tomography
- Computing with functions in the ball
- A Fast and Accurate Algorithm for Spherical Harmonic Analysis on HEALPix Grids with Applications to the Cosmic Microwave Background Radiation
- An optimal complexity spectral method for Navier--Stokes simulations in the ball