The Operator Group Generated by the One-dimensional Dirac System

In this paper, we construct a strongly continuous operator group generated by a one-dimensional Dirac operator acting in the space \(\mathbb{H}=\left(L_{2}[0,\pi]\right)^{2}\) . The potential is assumed to be summable. It is proved that this group is well-defined in the space \(\mathbb{H}\) and in the spaces \(\left(L_{\mu}[0,\pi]\right)^{2}\) , \(\mu\in(1,\infty)\) . In addition, we discuss estimates for the growth of the group as \(|t|\to+\infty\) .