Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 36, pp. 1-9.

Title: Normal extensions of a singular multipoint differential 
       operator of first order

Authors: Zameddin I. Ismailov (Karadeniz Technical Univ., Trabzon, Turkey)
         Rukiye Ozturk Mert (Hitit Univ. Corum, Turkey)

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 07, 2012.
Math Subject Classifications: 47A10, 47A20.
Key Words: Multipoint differential operators; selfadjoint and normal extension;
           spectrum.