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

David Marín; Marcel Nicolau

doi:10.1007/s00009-014-0393-2

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

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

Resum

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.

Idioma original	Anglès
Pàgines (de-a)	51-62
Nombre de pàgines	12
Revista	Mediterranean Journal of Mathematics
Volum	12
Número	1
DOIs	https://doi.org/10.1007/s00009-014-0393-2
Estat de la publicació	Publicada - de febr. 2014

Accés al document

10.1007/s00009-014-0393-2

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

Altres arxius i enllaços

Link to publication in Scopus

Com citar-ho

@article{340d244621564906ad96dade64ee6735,

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

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.",

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

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

year = "2014",

month = feb,

doi = "10.1007/s00009-014-0393-2",

language = "English",

volume = "12",

pages = "51--62",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

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

AU - Marín, David

AU - Nicolau, Marcel

PY - 2014/2

Y1 - 2014/2

N2 - 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 - 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

UR - http://www.scopus.com/inward/record.url?scp=84893164415&partnerID=8YFLogxK

U2 - 10.1007/s00009-014-0393-2

DO - 10.1007/s00009-014-0393-2

M3 - Article

SN - 1660-5446

VL - 12

SP - 51

EP - 62

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 1

ER -