Abstract
Given a \({\mathcal{C}^{2}}\) -function f on a compact riemannian manifold (X,g) we give a set of frequencies \({L=L_{f}(\varepsilon)}\) depending on a small parameter \({\varepsilon > 0}\) such that the relative L 2-error \({\frac{\|f-f^{L} \|}{\|f\|}}\) is bounded above by \({\varepsilon}\), where f L denotes the L-partial sum of the Fourier series f with respect to an orthonormal basis of L 2(X) constituted by eigenfunctions of the Laplacian operator Δ associated to the metric g.
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The authors were partially supported by the project MTM2011-26674-C02-01 of Ministerio de Economía y Competitividad of Spain / FEDER.
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Marín, D., Nicolau, M. A Priori L 2-Error Estimates for Approximations of Functions on Compact Manifolds. Mediterr. J. Math. 12, 51–62 (2015). https://doi.org/10.1007/s00009-014-0393-2
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DOI: https://doi.org/10.1007/s00009-014-0393-2