Inverse Spectral Problems for Sturm-Liouville Operators with Transmission Eonditions

This paper deals with the boundary value problem involving the differential equation  -ychr('39')chr('39')+q(x)y=lambda ysubject to the standard boundary conditions along with the following discontinuity conditions at a point  y(a+0)=a1y(a-0),  ychr('39')(a+0)=a2ychr('39')(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Liouville problem when there is a discontinuous condition on the closed interval. We show that the potential function and some coefficients of boundary conditions can be uniquely determined by the value of the potential on some interval and parts of two set of eigenvalues.

*The formula is not displayed correctly.