TY - JOUR

T1 - Inverse resonance scattering for massless Dirac operators on the real line

AU - Korotyaev , Evgeny

AU - Mokeev , Dmitrii

N1 - M1 - 1-2

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Dirac operators

KW - inverse problems

KW - resonances

KW - canonical systems

KW - compactly supported potentials

UR - https://content.iospress.com/articles/asymptotic-analysis/asy221786#b

U2 - 10.3233/ASY-221786

DO - 10.3233/ASY-221786

M3 - Article

VL - 132

SP - 83

EP - 130

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

ER -