The modified Parseval equality of Sturm-Liouville problems with transmission conditions
type: Item
instance of: scholarly article
title: The modified Parseval equality of Sturm-Liouville problems with transmission conditions
zbMATH Open document ID: 1397.34051
DOI: 10.1155/2013/619358
author: Mudan Bai
author: Jiong Sun
author: Siqin Yao
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We consider the Sturm-Liouville (S-L) problems with very general transmission conditions on a finite interval. Firstly, we obtain the sufficient and necessary condition for \(\lambda\) being an eigenvalue of the S-L problems by constructing the fundamental solutions of the problems and prove that the eigenvalues of the S-L problems are bounded below and are countably infinite. Furthermore, the asymptotic formulas of the eigenvalues and eigenfunctions of the S-L problems are obtained. Finally, we derive the eigenfunction expansion for Green's function of the S-L problems with transmission conditions and establish the modified Parseval equality in the associated Hilbert space.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 6950781
Wikidata QID: Q59003348
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/619358
OpenAlex ID: W2155938446
description: scientific article; zbMATH DE number 6950781