Inverse Sturm-Liouville problem with discontinuity conditions

This paper deals with the boundary value problem involving the dierential equation ly := -yʹʹ+qy = ?y, subject to the standard boundary conditions along with the following discontinuity conditions at a point a ?(0,?) y(a + 0) = a1y(a - 0), yʹ(a + 0) = a1-1yʹ(a - 0) + a2y(a - 0), where q(x), a1,a2 are real, q ? L2(0,? ) and ? is a parameter independent of x. We develop the Hochestadtʹs result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the nite interval where q(x) and q~(x) are analogous functions.