On the singular continuous spectrum of self-adjoint extensions
type: Item
instance of: scholarly article
title: On the singular continuous spectrum of self-adjoint extensions
zbMATH Open document ID: 0849.47005
DOI: 10.1007/PL00004547
published in: Mathematische Zeitschrift
publication date: 1996-02-12T00:00:00Z
full work available at URL: https://eudml.org/doc/174900
review text: Let \(H\) be a closed symmetric operator in the Hilbert space \({\mathcal H}\) with gap \(J\) and infinite deficiency indices. Given any open subset \(J_0\) of \(J\) we shall give explicitly a selfadjoint extension \(\widetilde {H}\) of \(H\) such that up to some discrete spectrum the spectrum of \(\widetilde {H}\) within the gap \(J\) of \(H\) is purely singular continuous and the singular continuous spectrum of \(\widetilde {H}\) within \(J\) equals the closure of \(J_0\) in \(J\).
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 838460
zbMATH Keywords: extension theory
zbMATH Keywords: symmetric operator
zbMATH Keywords: spectrum
zbMATH Keywords: singular continuous spectrum
author: J. Brasche
author: Hagen Neidhardt
MaRDI profile type: Publication
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OpenAlex ID: W4246964335
description: scientific article; zbMATH DE number 838460