  We solve the inverse problems to recover Dirac systems on an interval or
semiaxis from their spectral functions (matrix valued functions) for the case
of locally square-integrable potentials. Direct problems in terms of spectral
functions are treated as well. Moreover, we present necessary and sufficient
conditions on the given distribution matrix valued function to be a spectral
function of some Dirac system with a locally square-integrable potential.
Interesting connections with Paley-Wiener sampling measures appear in the case
of scalar spectral functions.
