Abstract :
It is proved that the set of products {u1u2} of solutions to homogeneous Schrödinger equations in a bounded domain D ⊂ Rd, d ≥ 3, where the set {u2|∂D} has a finite codimension in L2(∂D), is complete in L2(D). This result is used in proofs of the uniqueness of the solution to the inverse spectral problem with incomplete data, and of the uniqueness of the solution to the boundary inverse problems with incomplete data.
