# A Priori L 2-Error Estimates for Approximations of Functions on Compact Manifolds

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## Abstract

© 2014, Springer Basel. Given a C2-function f on a compact riemannian manifold (X, g) we give a set of frequencies L = Lf (ε) depending on a small parameter ε > 0 such that the relative L2-error(Formula presented.) is bounded above by ε, where fL denotes the L-partial sum of the Fourier series f with respect to an orthonormal basis of L2(X) constituted by eigenfunctions of the Laplacian operator Δ associated to the metric g.
Original language English 51-62 Mediterranean Journal of Mathematics 12 https://doi.org/10.1007/s00009-014-0393-2 Published - 1 Jan 2014

## Keywords

• Approximation theory
• Fourier analysis
• Laplacian operator
• Riemannian manifolds
• Spherical Harmonics