A three-point normal boundary value problem for an operator-differential equation
type: Item
instance of: scholarly article
title: A three-point normal boundary value problem for an operator-differential equation
zbMATH Open document ID: 0858.34052
DOI: 10.1007/BF02104571
published in: Siberian Mathematical Journal
publication date: 1996-08-14T00:00:00Z
review text: A densely defined closed operator \(B\) in a Hilbert space is called formally normal if \(D(B)\subseteq D(B^*)\) and \(|Bf|=|B^*f|\) for all \(f\in D(B)\). A formally normal operator is called maximal formally normal if it has no trivial formally normal extensions. The aim of this paper is to describe maximal formally normal extensions of the closure in \(L_2((0,1);H)\) of an operator of the form \(L_0'u=u'(t)+A(t)u(t)\), where \(A(t)=A_1\) for \(0\leq t<h\), \(A(t)=A_2\) for \(h\leq t\leq 1\), \(A_1\) and \(A_2\) are selfadjoint on \(H\), \(D(A_1)=D(A_2)=D(A)\), \(A_2\geq 0\), \(A_1\geq A_2+E\) and \(0<h\leq 1\). The description is done in terms of three-point boundary conditions.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34G99
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 917114
zbMATH Keywords: Hilbert space
zbMATH Keywords: formally normal operator
zbMATH Keywords: maximal formally normal extensions
zbMATH Keywords: three-point boundary conditions
Wikidata QID: Q115392789
author: Z. I. Ismailov
reviewed by: Radu Precup
MaRDI profile type: Publication
cites work: Q5337468
cites work: Normal extensions of formally normal operators
cites work: Generators of the Ring of Bounded Operators
cites work: Q5614166
cites work: Self-adjoint boundary problems for a second-order differential equation with unbounded operator coefficient
full work available at URL: https://doi.org/10.1007/bf02104571
OpenAlex ID: W2009253600
description: scientific article; zbMATH DE number 917114