Normal Extensions of a Singular Multipoint Differential Operator for First Order

Abstract

In this work, firstly in the direct sum of Hilbert spaces of vector-functions $L^2(H,(-\infty ,a_1))\oplus L^2(H,(a_2,b_2)){\oplus }^2(H,(a_3,+\infty ))$, $-\infty <a_1<a_2<b_2<a_3<+\infty$ 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 a selfadjoint operator coefficient $A_{k}k=1,2,3$ in any Hilbert space $H$, are described in terms of boundary values. Later structure of the spectrum of these extensions is investigated.

9 pages