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

© 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
Pages (from-to)	51-62
Journal	Mediterranean Journal of Mathematics
Volume	12
DOIs	https://doi.org/10.1007/s00009-014-0393-2
Publication status	Published - 1 Jan 2014

Keywords

Approximation theory
Fourier analysis
Laplacian operator
Riemannian manifolds
Spherical Harmonics

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title = "A Priori L 2-Error Estimates for Approximations of Functions on Compact Manifolds",

abstract = "{\textcopyright} 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.",

keywords = "Approximation theory, Fourier analysis, Laplacian operator, Riemannian manifolds, Spherical Harmonics",

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

year = "2014",

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

language = "English",

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T1 - A Priori L 2-Error Estimates for Approximations of Functions on Compact Manifolds

AU - Marín, David

AU - Nicolau, Marcel

PY - 2014/1/1

Y1 - 2014/1/1

N2 - © 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.

AB - © 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.

KW - Approximation theory

KW - Fourier analysis

KW - Laplacian operator

KW - Riemannian manifolds

KW - Spherical Harmonics

U2 - https://doi.org/10.1007/s00009-014-0393-2

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

M3 - Article

VL - 12

SP - 51

EP - 62

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

ER -