Basis properties of eigenfunctions of second-order differential operators with involution
type: Item
instance of: scholarly article
title: Basis properties of eigenfunctions of second-order differential operators with involution
zbMATH Open document ID: 1270.34195
DOI: 10.1155/2012/576843
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Consider the spectral problem \[ -u''(-x)+\alpha u''(x)=\lambda u(x),\tag{\(*\)} \] where \(\lambda\) is the spectral parameter. The authors prove the following results. Theorem 1. Suppose that \(\alpha^2\neq 1\). Then the eigenfunctions of \((*)\) satisfying \[ u(-1)= u(1) =0 \] form an orthonormal basis in \(L_2(-1,1)\). Theorem 2. Assume \(\alpha^2\neq 1\). Then the eigenfunctions of \((*)\) satisfying \[ u(-1)= u(1),\;u'(-1)= u'(1)\qquad(\text{periodic case}) \] or \[ u(-1)= -u(1),\;u'(-1)= -u'(1)\qquad(\text{antiperiodic case}) \] form orthonormal basis in \(L_2(-1,1)\).
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 6116419
zbMATH Keywords: Dirichlet
zbMATH Keywords: periodic
zbMATH Keywords: antiperiodic
Wikidata QID: Q58695577
author: Asylzat A. Kopzhassarova
author: Abdizhakhan M. Sarsenbi
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/576843
OpenAlex ID: W2060440157
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description: scientific article; zbMATH DE number 6116419