An Inverse Problem for a Sturm-Liouville Operator

If 0 is not a Dirichlet eigenvalue of the Sturm-Liouville operator − d2/dx2 + q(x) on (0, 1), then q(x) ∈ L2(0, 1) is uniquely determined by the data {u′j(0)}∞j = 1, where uj(x) solves −u″j(x) + q(x) uj(x) = ψj(x) 0 < x < 1uj(0) = 0uj(1) = 0 and {ψj(x)}∞j = 1 is a basis of L2(0, 1). Numerical approximations of q(x) using finite data are constructed.