Normal Extensions of a Singular Multipoint Differential Operator for First Order

Original · EN

In this work, firstly in the direct sum of Hilbert spaces of vector-functions L² (H,(-∞,a₁)) ⊕ L² (H,(a₂,b₂))⊕² (H,(a₃,+∞)), - ∞<a₁<a₂<b₂<a₃<+∞ all normal extensions of the minimal operator generated by linear singular multipoint formally normal differential expression l=(l₁,l₂,l₃),lₖ = d/dt+Aₖ with a selfadjoint operator coefficient Aₖ 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.