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Inverse resonance scattering for Dirac operators on the half-line. / Korotyaev, Evgeny; Mokeev, Dmitrii.
In: Analysis and Mathematical Physics, Vol. 11, No. 1, 32, 05.01.2021.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Inverse resonance scattering for Dirac operators on the half-line
AU - Korotyaev, Evgeny
AU - Mokeev, Dmitrii
N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
PY - 2021/1/5
Y1 - 2021/1/5
N2 - We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: (1) resonances are free parameters and a potential continuously depends on a resonance, (2) the forbidden domain for resonances is estimated, (3) asymptotics of resonance counting function is determined, (4) these results are applied to canonical systems.
AB - We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: (1) resonances are free parameters and a potential continuously depends on a resonance, (2) the forbidden domain for resonances is estimated, (3) asymptotics of resonance counting function is determined, (4) these results are applied to canonical systems.
KW - Canonical systems
KW - Compactly supported potentials
KW - Dirac operators
KW - Inverse problems
KW - Resonances
UR - http://www.scopus.com/inward/record.url?scp=85101961847&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/3eb2dd14-be88-3e41-b71f-51c7e8b43f70/
U2 - 10.1007/s13324-020-00453-5
DO - 10.1007/s13324-020-00453-5
M3 - Article
AN - SCOPUS:85101961847
VL - 11
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
SN - 1664-2368
IS - 1
M1 - 32
ER -
ID: 86154396