First-order selfadjoint singular differential operators in a Hilbert space of vector functions

Abstract

In this article, we give a representation of all selfadjoint extensions of the minimal operator generated by first-order linear symmetric multipoint singular differential expression, with operator coefficient in the direct sum of Hilbert spaces of vector-functions defined at the semi-infinite intervals. To this end we use the Calkin-Gorbachuk method. Finally, the geometry of spectrum set of such extensions is researched.

Keywords

• Multipoint singular differential expression
• deficiency indeces
• symmetric and selfadjoint differential operator
• spectrum