Vol. 14, No. 5, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
De Branges canonical systems with finite logarithmic integral

Roman V. Bessonov and Sergey A. Denisov

Vol. 14 (2021), No. 5, 1509–1556
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 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.

Keywords
Szegő class, canonical Hamiltonian systems, inverse problem, entropy
Mathematical Subject Classification 2010
Primary: 42C05, 34L40, 34A55
Milestones
Received: 14 June 2019
Revised: 9 December 2019
Accepted: 9 February 2020
Published: 22 August 2021
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