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De Branges canonical
systems with finite logarithmic integral
Roman V. Bessonov and Sergey A. Denisov |
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Vol. 14 (2021), No. 5, 1509–1556
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Abstract |
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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 Szegő 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. |
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Keywords
Szegő class, canonical Hamiltonian systems, inverse
problem, entropy
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Mathematical Subject Classification 2010
Primary: 42C05, 34L40, 34A55
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Milestones
Received: 14 June 2019
Revised: 9 December 2019
Accepted: 9 February 2020
Published: 22 August 2021
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Authors |
| Roman V. Bessonov | |
| St. Petersburg State
University St. Petersburg Russia |
St. Petersburg Department of Steklov
Mathematical Institute Russian Academy of Sciences St. Petersburg Russia |
| Sergey A. Denisov | |
| Department of Mathematics University of Wisconsin Madison, WI United States |
Keldysh Institute of Applied
Mathematics Russian Academy of Sciences Moscow Russia |
