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

David Marín; Marcel Nicolau

doi:https://doi.org/10.1007/s00009-014-0393-2

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

David Marín, Marcel Nicolau

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Given a C²-function f on a compact riemannian manifold (X, g) we give a set of frequencies L = L_f (ε) depending on a small parameter ε > 0 such that the relative L²-error(Formula presented.) is bounded above by ε, where f^L 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
Pages (from-to)	51-62
Number of pages	12
Journal	Mediterranean Journal of Mathematics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s00009-014-0393-2
Publication status	Published - Feb 2014

Keywords

Approximation theory
Fourier analysis
Laplacian operator
Riemannian manifolds
Spherical Harmonics

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https://doi.org/10.1007/s00009-014-0393-2

https://ddd.uab.cat/record/123652

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abstract = " 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.",

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author = "David Mar{\'i}n and Marcel Nicolau",

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AB - 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.

KW - Approximation theory

KW - Fourier analysis

KW - Laplacian operator

KW - Riemannian manifolds

KW - Spherical Harmonics

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EP - 62

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

IS - 1

ER -

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

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