Inverse spectral problems for Dirac operators with summable potentials

The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and the corresponding norming constants is established, and a complete solution of the inverse spectral problem is provided.