Generalized Fourier transform on an arbitrary triangular domain
type: Item
instance of: scholarly article
title: Generalized Fourier transform on an arbitrary triangular domain
zbMATH Open document ID: 1061.42021
author: Jiachang Sun
author: Huiyuan Li
published in: Advances in Computational Mathematics
publication date: 2005-03-04T00:00:00Z
review text: The authors consider generalized Fourier series on an arbitrary triangle \(\Omega\). Let \({\mathcal L}\) be a special second-order elliptic differential operator dependent on \(\Omega\). Then the eigenvalue problem \({\mathcal L}u=\lambda u\) in \(\Omega\), \(u=0\) on \(\partial \Omega\) has generalized sine functions (TSin) as eigenfunctions. The corresponding eigenvalue problem with homogeneous Neumann conditions has generalized cosine functions (TCos) as eigenfunctions. The orthogonality and completeness of both systems TSin and TCos are proved. Error estimates for the truncated generalized Fourier series are given in Sobolev norms. Finally, the convergence of these generalized Fourier series is demonstrated for some bivariate polynomials of lower degree.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C30
zbMATH DE Number: 2140541
zbMATH Keywords: generalized Fourier series
zbMATH Keywords: triangle
zbMATH Keywords: eigenfunction expansion
zbMATH Keywords: convergence
zbMATH Keywords: error estimates
zbMATH Keywords: Sobolev norm
zbMATH Keywords: generalized Fourier transform
zbMATH Keywords: generalized Fourier expansion
MaRDI profile type: Publication
full work available at URL: s10444-003-7667-8
OpenAlex ID: W2039047418
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DOI: 10.1007/S10444-003-7667-8
description: scientific article; zbMATH DE number 2140541