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.
Citation
Roman V. Bessonov. Sergey A. Denisov. "De Branges canonical systems with finite logarithmic integral." Anal. PDE 14 (5) 1509 - 1556, 2021. https://doi.org/10.2140/apde.2021.14.1509
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