Uniqueness of the interior transmission problem with partial information on the potential and eigenvalues
The paper deals with the boundary value problem \(B(q)\) of the form \[ y''+(\lambda-q(x))y=0, \quad 0<x<1, \quad y(0)=y(1)\cos\sqrt\lambda a-y'(1)\frac{\sin\sqrt\lambda a}{\sqrt\lambda}=0, \] where \(\lambda\) is the spectral parameter, \(q(x)\) is a real-valued function from \(L_2(0,1)\) and the positive parameter \(a\neq1\) is fixed. The authors study the inverse problem of recovering \(q(x)\) from the spectrum of \(B(q).\) In particular, they prove that \(q(x)\) is uniquely determined by a part of the real eigenvalues, provided that on a subinterval \(q(x)\) is known a priori. The connection between the length of this subinterval and the density of the real eigenvalues specified as well as the value of \(a\) is described.
scientific article; zbMATH DE number 6535777
scientific article