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Maximally Accretive Differential Operators of First Order in the Weighted Hilbert Spaces

Authors
  • Akbaba, Ü.1
  • Ipek Al, P.1
  • 1 Karadeniz Technical University, Faculty of Sciences, Department of Mathematics, Trabzon, 61080, Turkey , Trabzon (Turkey)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2707–2713
Identifiers
DOI: 10.1134/S1995080221120040
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

AbstractOur main goal in this paper is to investigate some spectral properties of all maximally accretive extensions of the minimal operator in the weighted Hilbert spaces of vector functions. We construct the minimal and maximal operators generated by the first order differential operator expression in the weighted Hilbert space of vector functions at finite interval with the use of standard technique. In this case, the minimal operator is accretive but not maximal. Using the Calkin–Gorbachuk method, the general form of all maximally accretive extensions of this minimal operator in terms of boundary conditions is obtained. We also investigate the structure of the spectrum set such maximally accretive extensions of this type of minimal operator.

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