Inverse problem for Dirac operators with a small delay

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.