Relationship Between Different Types of Inverse Data for the One-Dimensional Schrödinger Operator on a Half-Line

Resumo

Inverse dynamic, spectral, quantum, and acoustic scattering problems for the Schrödinger operator on a half-line are considered. The goal of the paper is to establish the relationship between different types of inverse data for these problems. The central objects, which serve as a source for all formulas, are the kernels of the so-called connecting operators and the corresponding Krein equations.