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Reflectionless Canonical Systems, I : Arov Gauge and Right Limits. / Bessonov, Roman; Lukić, Milivoje; Yuditskii, Peter.

In: Integral Equations and Operator Theory, Vol. 94, No. 1, 4, 01.03.2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Bessonov, R, Lukić, M & Yuditskii, P 2022, 'Reflectionless Canonical Systems, I: Arov Gauge and Right Limits', Integral Equations and Operator Theory, vol. 94, no. 1, 4. https://doi.org/10.1007/s00020-021-02683-z

APA

Bessonov, R., Lukić, M., & Yuditskii, P. (2022). Reflectionless Canonical Systems, I: Arov Gauge and Right Limits. Integral Equations and Operator Theory, 94(1), [4]. https://doi.org/10.1007/s00020-021-02683-z

Vancouver

Bessonov R, Lukić M, Yuditskii P. Reflectionless Canonical Systems, I: Arov Gauge and Right Limits. Integral Equations and Operator Theory. 2022 Mar 1;94(1). 4. https://doi.org/10.1007/s00020-021-02683-z

Author

Bessonov, Roman ; Lukić, Milivoje ; Yuditskii, Peter. / Reflectionless Canonical Systems, I : Arov Gauge and Right Limits. In: Integral Equations and Operator Theory. 2022 ; Vol. 94, No. 1.

BibTeX

@article{15dc59e012e34f23b208191328bb5730,
title = "Reflectionless Canonical Systems, I: Arov Gauge and Right Limits",
abstract = "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.",
keywords = "Almost periodic measures, Arov gauge, Breimesser–Pearson theorem, Canonical Hamiltonian systems, Krein–de Branges formula, Reflectionless, Ricatti equation, Breimesser-Pearson theorem, ABSOLUTELY CONTINUOUS-SPECTRUM, Krein-de Branges formula",
author = "Roman Bessonov and Milivoje Luki{\'c} and Peter Yuditskii",
note = "Bessonov, R., Luki{\'c}, 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",
year = "2022",
month = mar,
day = "1",
doi = "10.1007/s00020-021-02683-z",
language = "English",
volume = "94",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkh{\"a}user Verlag AG",
number = "1",

}

RIS

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