An n-dimensional Borg-Levinson theorem for singular potentials

We prove in this paper that the boundary spectral data, i.e. the Dirichlet eigenvalues and normal derivatives of the eigenfunctions at the boundary uniquely determines a potential in L-P on bounded domains. This result generalizes the result of Nachman, Sylvester and Uhlmann to unbounded potentials. This result can be viewed as a generalization of the classical one-dimensional Borg-Levinson theorem. (C) 2002 Elsevier Science (USA). All rights reserved.