Relationship between different types of inverse data for the one-dimensional Schrödinger operator on a half-line

Abstract

We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schrödinger operator on the half line. The goal of the paper is to establish the connections between different types of inverse data for these problems. The central objects which serve as a source for all formulaes are kernels of so-called connecting operators and Krein equations.

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Cited by in corpus (4)

• Boundary Control method and De Branges spaces. Schrödinger equation, Dirac system and Discrete Schrödinger operator
• On the relationship between Weyl functions of Jacobi matrices and response vectors for special dynamical systems with discrete time
• Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential
• On an inverse dynamic problem for the wave equation with a potential on a real line