• Mathematics
  • Published 2000

On the number of square integrable solutions and self-adjointness of symmetric first order systems of differential equations

@inproceedings{Lesch2000OnTN,
  title={On the number of square integrable solutions and self-adjointness of symmetric first order systems of differential equations},
  author={Matthias Lesch and Mark Mikhailovich Malamud},
  year={2000}
}
The main purpose of this paper is to investigate the formal deficiency indices ${\cal N}_{\pm}(I)$ of a symmetric first order system $$ Jf'+Bf=\lambda {\cal H} f $$ on an interval $I$, where $I=\mathbb{R}$ or $I=\mathbb{R}_\pm.$ Here $J,B,{cal H}$ are $n\times n$ matrix valued functions and the Hamiltonian ${\cal H}\ge 0$ may be singular even everywhere. We obtain two results for such a system to have minimal numbers ${\cal N}_\pm(\mathbb{R})=0$ (resp. ${\cal N}_\pm(\mathbb{R}_\pm)=n$) and a… CONTINUE READING