Electron. J. Diff. Equ., Vol. 2012 (2012), No. 36, pp. 1-9.

Normal extensions of a singular multipoint differential operator of first order

Zameddin I. Ismailov, Rukiye Ozturk Mert

In this work, we describe all normal extensions of the minimal operator generated by linear singular multipoint formally normal differential expression $l=(l_1,l_2,l_3)$, $l_k=\frac{d}{dt}+A_k$ with selfadjoint operator coefficients $A_k$ in a Hilbert space. This is done as a direct sum of Hilbert spaces of vector-functions
 L_2(H,(-\infty ,a_1))\oplus L_2(H,(a_2,b_2))
 \oplus L_2(H,(a_3,+\infty))
where $-\infty <a_1<a_2<b_2<a_3<+\infty$. Also, we study the structure of the spectrum of these extensions.

Submitted August 10, 2011. Published Match 7, 2012.
Math Subject Classifications: 47A10, 47A20.
Key Words: Multipoint differential operators; selfadjoint and normal extension; spectrum.

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Zameddin I. Ismailov
Department of Mathematics, Faculty of Sciences
Karadeniz Technical University
61080, Trabzon, Turkey
email: zameddin@yahoo.com
Rukiye Öztürk Mert
Department of Mathematics, Art and Science Faculty
Hitit University
19030, Corum, Turkey
email: rukiyeozturkmert@hitit.edu.tr

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