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arXiv · 1903.05622

De Branges canonical systems with finite logarithmic integral

Roman Bessonov·Sergey Denisov
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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 Szego 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.

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Roman Bessonov, Sergey Denisov. 2019-03-13. De Branges canonical systems with finite logarithmic integral. https://doi.org/10.2140/apde.2021.14.1509

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