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

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.

Show me the PDF file (214 KB), TEX file, and other files for this article.

Return to the EJDE web page
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