An Inverse Sturm–Liouville Problem with Mixed Given Data

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 ( 1/2,1 ), then a single spectrum suffices to determine $q( x )$ on the interval ( 0,1/2 ).