Inverse spectral problems for the Sturm-Liouville operator with discontinuity

Abstract

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge 1/2$, then parts of two spectra can uniquely determine the potential and all parameters in discontinuous conditions and boundary conditions. For the case $b<1/2$, parts of either one or two spectra can uniquely determine the potential and a part of parameters.

13 pages

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• Inverse spectral problems for non-self-adjoint Sturm-Liouville operators with discontinuous boundary conditions