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+۰)=a y(d-۰), y'(d+۰)=ay'(d-۰)+b y(d-۰). In this problem q(x), d, a , b are real, qin L^۲(۰,pi), din(۰,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).