Operator group construction and equivalent bases in one-dimensional Dirac spectral problem

The talk deals with the construction of a strongly continuous operator group generated by a one-dimensional Dirac operator acting in the space $\mathbb{H}=(L_2[0,\pi])^2$. The potential is assumed to be summable. It will be shown that this group is defined in the space $\mathbb{H}=(L_2[0,\pi])^2$ and in the spaces $(L_\mu[0,\pi])^2,\mu\in(1,\infty)$.
In the course of the construction of the group, an interesting in itself question arose about the equivalence of two bases obtained from systems of eigenfunctions and adjoint functions of Dirac operators with the same separated boundary conditions and different summable potentials. We will show the equivalence of these systems in the spaces $L_{\mu}[0,\pi]$ for all $\mu\in(1,\infty)$. The idea of the proof goes back to the results of A.M. Sedletsky on boundedness and bounded reversibility of basis substitution operators from exponents.