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We give a complete description of the set of spectral data (eigenvalues andspecially introduced norming constants) for Sturm--Liouville operators on theinterval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$and suggest an algorithm reconstructing the potential from the spectral datathat is based on Krein's accelerant method.

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials