Mediterranean Journal of Mathematics

, Volume 12, Issue 1, pp 51–62 | Cite as

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



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.

Mathematics Subject Classification (1991)

Primary 42C Secondary 58C40 33C45 68U05 


Fourier analysis Riemannian manifolds Laplacian operator Spherical Harmonics Approximation theory 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain

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