Inverse Spectral problem for the Sturm-Liouville Operator with Eigenvalue Parameter Dependent Boundary Conditions

To solve the inverse problem for the Sturm-Liouville operator with eigenvalue parameter dependent boundary conditions we reconstruct the spectral distribution function from two spectra of the boundary-value problems with equal Θ(λ) and different real constants in the boundary conditions. The well-known results of A.V. Strauss [] concerning the connection between the eigenvalue problems with the spectral parameter in the boundary conditions and the theory of generalized resolvents is used.