Electron. J. Diff. Equ., Vol. 2013 (2013), No. 129, pp. 1-11.

Selfadjoint extensions of a singular multipoint differential operator of first order

Zameddin I. Ismailov, Rukiye Ozturk Mert

Abstract:
In this work, we describe all selfadjoint extensions of the minimal operator generated by linear singular multipoint symmetric differential expression $l=(l_1,l_2,l_3)$, $l_k=i\frac{d}{dt}+A_k$ with selfadjoint operator coefficients $A_k$, $k=1,2,3$ 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 April 29, 2013. Published May 27, 2013.
Math Subject Classifications: 47A10, 47A20.
Key Words: Quantum field theory; spectrum; multipoint differential operators; selfadjoint extension.

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