Inverse nodal problems of discontinuous Sturm-Liouville operator
The paper deals with the Sturm-Liouville equation on a finite interval (namely, on \((0,1)\)), with jump conditions at an internal point of the interval, of the type \[ y(1/2+0)=a_1 y(1/2-0), y'(1/2+0)=a_1^{-1} y'(1/2-0) + a_2 y(1/2-0). \] Supplemented with boundary conditions at the ends of the interval, the equation determines a self-adjoint operator. The author studies the inverse problem consisting in the reconstruction of the operator (i.e., the potential, the constants involved in the boundary conditions, and the jump parameters \(a_1\) and \(a_2\)) from the set of zeros of the eigenfunctions (nodes). He introduces the notions of subnodal set and twin subnodal set and proves that a dense subnodal set determines uniquely the operator (the potential and the parameters). The reconstruction formulas are given and the stability of the reconstruction is discussed.
scientific article; zbMATH DE number 6140139