An inverse three spectra problem for Sturm–Liouville operators

Abstract

In this paper, we consider the inverse three spectra problems of recovering the Sturm-Liouville equation by the spectra of the Neumann-Dirichlet boundary value problem on [0, 1], the Neumann-Robin problem on [0, 1/2], and the Robin-Dirichlet problem on [1/2, 1], where the two Robin parameters at the interior node x = 1/2 are considered to be different. The algorithm of construction is presented and sufficient conditions for three sequences to be the spectral data of the mentioned boundary problems are given. Primary 34A55; secondary 34L05; 34B24 MSC:

Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator

“…The most complete results on inverse problems of spectral analysis have been obtained for self-adjoint Sturm-Liouville operators. Those results include uniqueness theorems, algorithms for constructive solution, spectral data characterization, local solvability and stability (see studies [5][6][7][8][9][10][11] and the references therein).…”