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

Abstract:
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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