Inverse problem for Dirac operators with a small delay

TL;DR

This paper investigates inverse spectral problems for Dirac operators with a small delay, revealing limitations of spectral data for potential recovery and exploring related inverse problems with implications for delayed differential operators.

Contribution

It introduces new insights into the inverse spectral problem for Dirac operators with delay, showing two spectra are insufficient for potential recovery and analyzing related inverse problems.

Findings

Two spectra are insufficient for potential recovery.

Eigenvalue behavior is characterized for delayed Dirac operators.

Results inform future research on inverse problems with delays.

Abstract

This paper addresses inverse spectral problems associated with Dirac-type operators with a constant delay, specifically when this delay is less than one-third of the interval length. Our research focuses on eigenvalue behavior and operator recovery from spectra. We find that two spectra alone are insufficient to fully recover the potentials. Additionally, we consider the Ambarzumian-type inverse problem for Dirac-type operators with a delay. Our results have significant implications for the study of inverse problems related to the differential operators with a constant delay and may inform future research directions in this field.