Property C and uniqueness theorems for multidimensional inverse spectral problems

AbstractA simple proof is given of the uniqueness theorem for the multidimensional inverse spectral problem. This problem consists in finding the potential from the set of the corresponding eigenvalues and the traces of normal derivatives of the eigenfunctions on the boundary. The proof is based on property C for Schrödinger operators. The smoothness assumption on q(x) is weaker than in the earlier results: it is assumed that q∈L2(D)