Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operatorbüschel
type: Item
instance of: scholarly article
title: Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operatorbüschel
zbMATH Open document ID: 0538.47004
DOI: 10.1007/BF01163872
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173518
review text: We consider irregular eigenvalue problems of the form \[ (1)\quad \ell(y,\lambda)=\lambda^ ny+\sum^{n}_{j=1}(\sum^{j}_{k=0}p_{kj}(x)y^{(k)})\lambda^{n-j}=0,\quad(2)\quad U_{\nu}(y)=0,\quad 1\leq \nu \leq n \] with two-point boundary conditions, \(p_{jj}\in {\mathbb{C}}\) for 1\(\leq j\leq n\) and \(p_{nn}\neq 0\). We assume that all roots \(\omega_ 1,...,\omega_ n\) of the characteristic equation \(1+\sum^{n}_{j=1}p_{jj}\omega^ j=0\) are nonzero and have different arguments. If some additional conditions on (1), (2) are fulfilled, the system of all eigen- and associated functions of (1), (2) is complete in \(L_ 2[0,1]\).
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 3855794
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: two-point boundary conditions
author: Gerhard Freiling
MaRDI profile type: Publication
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OpenAlex ID: W438706740
description: scientific article; zbMATH DE number 3855794