inverse sturm-liouville problems with transmission and spectral parameter boundary conditions

this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by defining 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) - tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).