Reconstruction of Differential Operators with Frozen Argument

Abstract

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.

Keywords

• differential operators
• Sturm–Liouville-type operators
• inverse problems
• rank-one perturbations
• frozen argument