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 languageEnglish
Pages (from-to)51-62
JournalMediterranean Journal of Mathematics
Volume12
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

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

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