Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment

Ballesteros M, Franco G, Naumkin I, Schulz-Baldes H (2023)

Publication Language: English

Publication Type: Journal article

Publication year: 2023

Journal

Communications in Contemporary Mathematics World Scientific Publishing

Abstract

This paper proves new results on spectral and scattering theory for matrix-valued Schr\"odinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson theorem is proved, in which a relation between scattering data and spectral properties (bound and half bound states) of the corresponding Hamiltonians is derived. The proof is based on stationary scattering theory with prominent use of Jost solutions at complex energies that are controlled by Volterra-type integral equations.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM) MX Mexico (MX)

How to cite

APA:

Ballesteros, M., Franco, G., Naumkin, I., & Schulz-Baldes, H. (2023). Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment. Communications in Contemporary Mathematics.

MLA:

Ballesteros, Miguel, et al. "Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment." Communications in Contemporary Mathematics (2023).

BibTeX: Download