Opuscula Math. 29, no. 4 (2009), 399-414
Multipoint normal differential operators of first order
Zameddin I. Ismailov
Abstract.
In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
Keywords:
differential operator, formally normal and normal operator, multipoint minimal and maximal operators, extension, selfadjoint, accretive and unitary operators, class of compact operators, spectrum of an operators and its discreteness, asymptotics of eigenvalues, direct sum of spaces and operators.
Mathematics Subject Classification:
47A20.
About the authors ▼
Zameddin I. Ismailov
Karadeniz Technical University, Department of Mathematics, Faculty of Arts and Sciences, 61080 Trabzon, Turkey
About the article ▼
Received: 2009-09-04.
Revised: 2009-08-16.
Accepted: 2009-08-22.
Cite this article as ▼
Zameddin I. Ismailov, Multipoint normal differential operators of first order, Opuscula Math. 29, no. 4 (2009), 399-414,
http://dx.doi.org/10.7494/OpMath.2009.29.4.399.
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