Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions

This paper deals with the boundary value problem involving the di erential equation ly := -y + qy = λy; subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d + 0) = ay(d - 0), y (d + 0) = ay (d - 0) + by(d - 0): In this problem q(x), d, a, b are real, q Є L²(0,п), d² (0,п) and λ is a parameter independent of x. By de ning a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt s result based on transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x) -~q(x) in the nite interval, where ~q(x) is an analogous function with q(x).