Small-energy analysis for the selfadjoint matrix Schroedinger operator on the half line. II

Abstract

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a second moment, it is shown that the corresponding scattering matrix is differentiable at zero energy. An explicit formula is provided for the derivative of the scattering matrix at zero energy. The previously established results when the potential has only the first moment are improved when the second moment exists, by presenting the small-energy asymptotics for the related Jost matrix, its inverse, and various other quantities relevantc to the corresponding direct and inverse scattering problems.

This published version has been edited to improve the presentation of the results

References in corpus (2)

• Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line
• High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line

Cited by in corpus (4)

• Scattering Theory for the matrix Schrödinger operator on the half line with general boundary conditions
• Trace Identities for the matrix Schrödinger operator on the half line with general boundary conditions
• The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions
• $L^p-L^{p^{\prime }}$ estimates for matrix Schrödinger equations