Mogilevskii, V. I. On exit space extensions of symmetric operators with applications to first order symmetric systems. (English) Zbl 1289.47046 Methods Funct. Anal. Topol. 19, No. 3, 268-292 (2013). The author continues his work (V. Mogilevskii [Methods Funct. Anal. Topol. 12, No. 3, 258–280 (2006; Zbl 1125.47015)]) on the method of abstract boundary conditions in the extension theory of symmetric operators and relations with non-equal deficiency numbers. In particular, he gives a description, in terms of the Weyl functions, of the densely defined operators and the exit space operator-extensions (among relations-extensions). The general results are applied to (possibly, non-Hamiltonian) symmetric differential systems \(Jy'-B(t)y=\Delta (t)f(t)\), \(t\in [a,b]\), where \(B(t)=B(t)^*\), \(\Delta (t)\geq 0\). The system is considered in the quotient space corresponding to the quasi-inner product \(\langle f,g\rangle =\int\limits_a^b \Delta (t)f(t)[g(t)]^*\,dt\). Reviewer: Anatoly N. Kochubei (Kyïv) Cited in 6 Documents MSC: 47B25 Linear symmetric and selfadjoint operators (unbounded) 47E05 General theory of ordinary differential operators 34B08 Parameter dependent boundary value problems for ordinary differential equations 34L05 General spectral theory of ordinary differential operators 47A06 Linear relations (multivalued linear operators) Keywords:symmetric operator; symmetric relation; deficiency numbers; exit space extensions; Weyl function; first order symmetric systems Citations:Zbl 1125.47015 PDFBibTeX XMLCite \textit{V. I. Mogilevskii}, Methods Funct. Anal. Topol. 19, No. 3, 268--292 (2013; Zbl 1289.47046)