Irregular eigenvalue-problems on the half-axis
type: Item
instance of: scholarly article
title: Irregular eigenvalue-problems on the half-axis
zbMATH Open document ID: 0654.34019
DOI: 10.1007/BF03323216
author: Walter Eberhard
published in: Results in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Singular differential operators \(L:D\to L^ 2({\mathbb{R}}^+_ 0)\) generated by the differential expression \(\ell y:=y^{(n)}+\sum^{n}_{k=2}p_ ky^{(n-k)}\) and boundary conditions \(U_ i\), \(1\leq i\leq m\) for \(D=\{y| y\in C^{n-1}({\mathbb{R}}^+_ 0)\cap L^ 2({\mathbb{R}}^+_ 0),y^{(n-1)}\) a.c., \(U_ iy=0\), \(1\leq i\leq m\), \(\ell y\in L^ 2({\mathbb{R}}^+_ 0)\}\) are investigated where \(m,n/2\leq m\leq n-1\), is an integer. For compact intervals the resp. operators are called irregular and have been considered by Hromov, Freiling and the author. For the singular case is proved that the resolvent of L is an integral operator, but not being bounded resp. the eigenvalue-parameter \(\lambda\). An analogon of the expansion-formula of Weyl-Titchmarsh is derived for a certain well-defined class of analytic functions.
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4067363
zbMATH Keywords: indefinite eigenvalue problems
zbMATH Keywords: irregular eigenvalue problems
zbMATH Keywords: Singular differential operators
zbMATH Keywords: expansion-formula of Weyl-Titchmarsh
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03323216
OpenAlex ID: W2054076791
description: scientific article; zbMATH DE number 4067363