In this paper we consider the inverse Sturm{Liouville problems with a fi nite number of discontinuities at interior points. We develop the Hochestadt's result based on transformation operator for Sturm-Liouville problem with finite number of transmission conditions. Furthermore, we establish a formula for q(x) ~q(x) in the fi nite interval, where ~q(x) and q(x) are analogous potential functions with different operators.
