An Inverse Sturm–Liouville Problem with Mixed Given Data

Source abstract

In general the potential function $q( x )$ in a Sturm–Liouville problem is uniquely determined by two spectra. It is shown here that if $q( x )$ is prescribed over the interval $\left( {\frac{1}{2},1} \right)$, then a single spectrum suffices to determine $q( x )$ on the interval $\left( {0,\tfrac{1}{2}} \right)$.