Counterexamples in indefinite Sturm--Liouville problems
type: Item
instance of: scholarly article
title: Counterexamples in indefinite Sturm--Liouville problems
zbMATH Open document ID: 0942.34022
author: N. L. Abasheieva
author: S. G. Pyatkov
published in: Siberian Advances in Mathematics
publication date: 2000-04-13T00:00:00Z
review text: The authors consider the spectral problem \[ -u''(x)=\lambda\omega(x) u(x),\quad x\in(-1,1), \quad u(-1)=u(1)=0, \] with \(\omega(x) \) being a sign-changing function. They describe some particular classes of functions \(\omega(x) \) for which the eigenfunctions to this problem do not form a~Riesz basis for the weighted space \(L_{2,\omega}(-1,1)\) under the norm \(\|u\|_{L_{2 ,\omega}(-1,1)}=\|\sqrt{|\omega|}u\|_{L_2 (-1,1)}\).
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 1431674
zbMATH Keywords: indefinite spectral problems
zbMATH Keywords: Riesz basis
zbMATH Keywords: sufficient conditions
zbMATH Keywords: counterexamples
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1431674