Estimates of norms of eigenfunctions of the Sturm-Liouville problem in Sobolev spaces
type: Item
instance of: scholarly article
title: Estimates of norms of eigenfunctions of the Sturm-Liouville problem in Sobolev spaces
zbMATH Open document ID: 1057.34106
DOI: 10.1023/A:1023271607674
author: Ya. G. Buchaev
published in: Mathematical Notes
publication date: 2004-11-15T00:00:00Z
review text: The eigenfunctions of the Sturm-Liouville problem with Dirichlet boundary conditions on \([0,1]\) for the equation \(-y''+q(x)y=\lambda\rho(x)y\), \(q\in L_{1}(0,1)\), \(0<m<\rho(x)<M<\infty\), are studied. It is assumed that the eigenfunctions are normed in \(L_{q}((0,1);\rho(x))\), \(q\geq1\). Their norms in the Sobolev spaces \(W_{p}^{\theta}\), \(p\geq1\), \(0\leq\theta\leq2\), are estimated.
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 2115603
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: norm of eigenfunctions
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Dirichlet condition
MaRDI profile type: Publication
full work available at URL: a:1023271607674
OpenAlex ID: W140157611
description: scientific article; zbMATH DE number 2115603