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• W4385255518 abstract "Abstract The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently approximate it by a Fourier series, which can be evaluated efficiently via fast Fourier transforms. Similar approaches have emerged for approximation problems on the disk, the ball, and the cylinder. In this paper, we introduce a generalized DFS method applicable to various manifolds, including all the above-mentioned cases and many more, such as the rotation group. This approach consists in transforming a function defined on a manifold to the torus of the same dimension. We show that the Fourier series of the transformed function can be transferred back to the manifold, where it converges uniformly to the original function. In particular, we obtain analytic convergence rates in case of Hölder-continuous functions on the manifold." @default.
• W4385255518 created "2023-07-26" @default.
• W4385255518 creator A5016136976 @default.
• W4385255518 creator A5054449081 @default.
• W4385255518 date "2023-07-25" @default.
• W4385255518 modified "2023-10-01" @default.
• W4385255518 title "A double Fourier sphere method for d-dimensional manifolds" @default.
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• W4385255518 doi "https://doi.org/10.1007/s43670-023-00064-8" @default.
• W4385255518 hasPublicationYear "2023" @default.
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