Spectral properties of ordinary differential operators admitting special decompositions
type: Item
instance of: scholarly article
title: Spectral properties of ordinary differential operators admitting special decompositions
zbMATH Open document ID: 1489.47069
published in: Communications on Pure and Applied Analysis
publication date: 2021-06-16T00:00:00Z
review text: The paper deals with spectral properties of ordinary differential operators related to expressions of the form \(D^\epsilon + a\). Here, \(a\in \mathbb{R}\) and \(D^\epsilon\) denotes a composition of \(\partial\) and \(\partial^+\) according to the signs in the multi-index \(\epsilon\), where \(\partial\) is a first order linear differential expression, called delta-derivative, and \(\partial^+\) is its formal adjoint in an appropriate \(L_2\) space. In particular, Sturm-Liouville operators that admit the decomposition of the type \(\partial^+\partial + a\) are considered. The authors propose an approach, based on weak delta-derivatives and delta-Sobolev spaces, which is particularly useful in the study of the operators \(D^\epsilon + a\). Finally, they examine a number of examples of operators, which are of the relevant form, naturally arising in analysis of classical orthogonal expansions.
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 7359976
zbMATH Keywords: self-adjoint operator
zbMATH Keywords: essentially self-adjoint operator
zbMATH Keywords: weak derivative
zbMATH Keywords: Sobolev space
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: Friedrichs extension
author: Krzysztof Stempak
reviewed by: A. S. Makin
MaRDI profile type: Publication
full work available at URL: cpaa.2021054
OpenAlex ID: W3147465505
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DOI: 10.3934/CPAA.2021054
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article; zbMATH DE number 7359976