A UNIQUENESS THEOREM FOR STURM-LIOUVILLE OPERATORS WITH EIGENPARAMETER DEPENDENT BOUNDARY CONDITIONS

In this paper, we discuss the inverse problem for Sturm-Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval [0,1]. Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on [0, + 1/2 + alpha/2] for some alpha is an element of [0,1), then the potential q(x) on the interval [0,1] and fractional linear function a(2)lambda+b(2)/c(2)lambda+d(2) of the boundary condition are, uniquely determined by a subset S subset of sigma(L) and fractional linear function a(1)lambda+b(1)/c(1)lambda+d(1) of the boundary condition.