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Reflectionless Canonical Systems, I : Arov Gauge and Right Limits. / Bessonov, Roman; Lukić, Milivoje; Yuditskii, Peter.
в: Integral Equations and Operator Theory, Том 94, № 1, 4, 01.03.2022.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Reflectionless Canonical Systems, I
T2 - Arov Gauge and Right Limits
AU - Bessonov, Roman
AU - Lukić, Milivoje
AU - Yuditskii, Peter
N1 - Bessonov, R., Lukić, M. & Yuditskii, P. Reflectionless Canonical Systems, I: Arov Gauge and Right Limits. Integr. Equ. Oper. Theory 94, 4 (2022). https://doi.org/10.1007/s00020-021-02683-z
PY - 2022/3/1
Y1 - 2022/3/1
N2 - In spectral theory, j-monotonic families of 2 × 2 matrix functions appear as transfer matrices of many one-dimensional operators. We present a general theory of such families, in the perspective of canonical systems in Arov gauge. This system resembles a continuum version of the Schur algorithm, and allows to restore an arbitrary Schur function along the flow of associated boundary values at infinity. In addition to results in Arov gauge, this provides a gauge-independent perspective on the Krein–de Branges formula and the reflectionless property of right limits on the absolutely continuous spectrum. This work has applications to inverse spectral problems which have better behavior with respect to a normalization at an internal point of the resolvent domain.
AB - In spectral theory, j-monotonic families of 2 × 2 matrix functions appear as transfer matrices of many one-dimensional operators. We present a general theory of such families, in the perspective of canonical systems in Arov gauge. This system resembles a continuum version of the Schur algorithm, and allows to restore an arbitrary Schur function along the flow of associated boundary values at infinity. In addition to results in Arov gauge, this provides a gauge-independent perspective on the Krein–de Branges formula and the reflectionless property of right limits on the absolutely continuous spectrum. This work has applications to inverse spectral problems which have better behavior with respect to a normalization at an internal point of the resolvent domain.
KW - Almost periodic measures
KW - Arov gauge
KW - Breimesser–Pearson theorem
KW - Canonical Hamiltonian systems
KW - Krein–de Branges formula
KW - Reflectionless
KW - Ricatti equation
KW - Breimesser-Pearson theorem
KW - ABSOLUTELY CONTINUOUS-SPECTRUM
KW - Krein-de Branges formula
UR - http://www.scopus.com/inward/record.url?scp=85122083267&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/a3b35761-00e4-3dd6-9bac-1b6e73a69bea/
U2 - 10.1007/s00020-021-02683-z
DO - 10.1007/s00020-021-02683-z
M3 - Article
AN - SCOPUS:85122083267
VL - 94
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 1
M1 - 4
ER -
ID: 94392791