Inverse resonance scattering for massless Dirac operators on the real line

Article type: Research Article

Authors: Korotyaev, Evgeny^{a; b; *} | Mokeev, Dmitrii^b

Affiliations: [a] Department of Analysis, Saint-Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia | [b] HSE University, 3A Kantemirovskaya ulitsa, St. Petersburg, 194100, Russia

Correspondence: [*] Corresponding author. E-mails: [email protected], [email protected].

Abstract: We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems: in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e. resonances). Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain the sequence of zeros of the reflection coefficient for another compactly supported potential, 2) the set of “isoresonance potentials” is described, 3) the forbidden domain for resonances is estimated, 4) asymptotics of the resonances counting function is determined, 5) these results are applied to canonical systems.

Keywords: Dirac operators, inverse problems, resonances, canonical systems, compactly supported potentials

DOI: 10.3233/ASY-221786

Journal: Asymptotic Analysis, vol. 132, no. 1-2, pp. 83-130, 2023