Opuscula Math. 29, no. 4 (2009), 399-414

Opuscula Mathematica

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.

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  • Zameddin I. Ismailov
  • Karadeniz Technical University, Department of Mathematics, Faculty of Arts and Sciences, 61080 Trabzon, Turkey
  • Received: 2009-09-04.
  • Revised: 2009-08-16.
  • Accepted: 2009-08-22.
Opuscula Mathematica - cover

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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