DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL

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DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL. / Bessonov, Roman V.; Denisov, Sergey A.

In: Analysis and PDE, Vol. 14, No. 5, 2021, p. 1509-1556.

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Bessonov, Roman V. ; Denisov, Sergey A. / DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL. In: Analysis and PDE. 2021 ; Vol. 14, No. 5. pp. 1509-1556.

BibTeX

@article{077e5a26eba44e63b2b4e0f0300c7a46,

title = "DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL",

abstract = "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 Szeg{\^o} 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.",

keywords = "canonical Hamiltonian systems, entropy, inverse problem, SzegO class",

author = "Bessonov, {Roman V.} and Denisov, {Sergey A.}",

year = "2021",

doi = "10.2140/apde.2021.14.1509",

language = "English",

volume = "14",

pages = "1509--1556",

journal = "Analysis and PDE",

issn = "2157-5045",

publisher = "Mathematical Sciences Publishers",

number = "5",

}

RIS

TY - JOUR

T1 - DE BRANGES CANONICAL SYSTEMS WITH FINITE LOGARITHMIC INTEGRAL

AU - Bessonov, Roman V.

AU - Denisov, Sergey A.

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 -

ID: 94393039