Comments on eigenfunction expansions of discontinuous Sturm-Liouville systems
type: Item
instance of: scholarly article
title: Comments on eigenfunction expansions of discontinuous Sturm-Liouville systems
zbMATH Open document ID: 0716.34026
DOI: 10.1016/0893-9659(89)90060-8
author: Mei Kobayashi
published in: Applied Mathematics Letters
publication date: 1989-01-01T00:00:00Z
review text: Consider the eigenvalue problem \(-y''+q(x)y=\lambda y\) on \(0\leq x\leq \pi\) satisfying the symmetric boundary conditions \(hy(0)- y'(0)=hy(\pi)+y'(\pi)=0\) with two symmetric discontinuities at \(x=d_ 1\) and \(x=d_ 2=\pi -d_ 1\), satisfying the jump conditions: \(y(d_ 1+)=ay(d_ 1-),\quad y(d_ 2-)=ay(d_ 2+),\quad y(d_ 1+)=a^{- 1}y(d_ 1-)+by(d_ 1-),\quad y'(d_ 2-)=a^{-1}y(d_ 2+)-by(d_ 2+),\) where \(a>0\) and b are the jumb constants, h is a boundary constant and q is integrable on [0,\(\pi\) ]. The authors shows that any function f such that f and \(f'\) are sectionally continuous on (0,\(\pi\)) with sections (0,d), (d,\(\pi\)-d), (\(\pi\)-d,\(\pi\)) has a Fourier series-type expansion in terms of the eigenfunctions of the above problem.
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L10
zbMATH DE Number: 4179816
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: Fourier series-type expansion
MaRDI profile type: Publication
full work available at URL: 0893-9659(89)90060-8
OpenAlex ID: W1995943270
cites work: The inverse Sturm-Liouville problem with symmetric potentials
cites work: Q5838785
cites work: An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials
cites work: Eigenfunction Expansions: A Discontinuous Version
cites work: Discontinuous inverse eigenvalue problems
cites work: Inverse Sturm-Liouville problems with two discontinuities
description: scientific article; zbMATH DE number 4179816