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