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De Branges Canonical Systems with Finite Logarithmic Integral. / Bessonov, Roman V.; Denisov, Sergey A.
Extended Abstracts Fall 2019: Spaces of Analytic Functions: Approximation, Interpolation, Sampling. Springer Nature, 2021. стр. 37-41 (Trends in Mathematics; Том 12).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике › научная › Рецензирование
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TY - CHAP
T1 - De Branges Canonical Systems with Finite Logarithmic Integral
AU - Bessonov, Roman V.
AU - Denisov, Sergey A.
N1 - Publisher Copyright: © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - Krein–de Branges spectral theory provides a correspondence between canonical Hamiltonian systems and measures on the real line with finite Poisson integral. We revisit this area by giving a description of canonical Hamiltonian systems whose spectral measures have logarithmic integral converging over the real line. Our result can be viewed as a spectral version of the classical Szegő theorem in the theory of polynomials orthogonal on the unit circle. It extends Krein–Wiener completeness theorem, a key fact in the prediction of stationary Gaussian processes.
AB - Krein–de Branges spectral theory provides a correspondence between canonical Hamiltonian systems and measures on the real line with finite Poisson integral. We revisit this area by giving a description of canonical Hamiltonian systems whose spectral measures have logarithmic integral converging over the real line. Our result can be viewed as a spectral version of the classical Szegő theorem in the theory of polynomials orthogonal on the unit circle. It extends Krein–Wiener completeness theorem, a key fact in the prediction of stationary Gaussian processes.
UR - http://www.scopus.com/inward/record.url?scp=85119698907&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-74417-5_6
DO - 10.1007/978-3-030-74417-5_6
M3 - Article in an anthology
AN - SCOPUS:85119698907
SN - 978-3-030-74416-8
T3 - Trends in Mathematics
SP - 37
EP - 41
BT - Extended Abstracts Fall 2019
PB - Springer Nature
ER -
ID: 94392866