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 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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Cited by in corpus (4)

• Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials
• Trace formulas and inverse spectral theory for generalized indefinite strings
• Sobolev norms of $L^2$-solutions to NLS
• On the absolutely continuous spectrum of generalized indefinite strings II