TY - JOUR

T1 - DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL

AU - Bessonov, Roman V.

AU - Denisov, Sergey A.

N1 - Publisher Copyright: © 2021 2021 Mathematical Sciences Publishers. All Rights Reserved.

PY - 2021

Y1 - 2021

N2 - Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on the real line with finite Poisson integral. We further develop this area by giving a description of canonical Hamiltonian systems whose spectral measures have logarithmic integral converging over the real line. This result can be viewed as a spectral version of the classical Szegô theorem in the theory of polynomials orthogonal on the unit circle. It extends the Krein-Wiener completeness theorem, a key fact in the prediction of stationary Gaussian processes.

AB - Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on the real line with finite Poisson integral. We further develop this area by giving a description of canonical Hamiltonian systems whose spectral measures have logarithmic integral converging over the real line. This result can be viewed as a spectral version of the classical Szegô theorem in the theory of polynomials orthogonal on the unit circle. It extends the Krein-Wiener completeness theorem, a key fact in the prediction of stationary Gaussian processes.

KW - canonical Hamiltonian systems

KW - entropy

KW - inverse problem

KW - SzegO class

UR - http://www.scopus.com/inward/record.url?scp=85114839115&partnerID=8YFLogxK

U2 - 10.2140/apde.2021.14.1509

DO - 10.2140/apde.2021.14.1509

M3 - Article

AN - SCOPUS:85114839115

VL - 14

SP - 1509

EP - 1556

JO - Analysis and PDE

JF - Analysis and PDE

SN - 2157-5045

IS - 5

ER -