Title: Szego theorem for measures on the real line: optimal results and applications. Abstract: Measures on the unit circle for which the logarithmic integral converges can be characterized in many different ways: e.g., through their Schur parameters or through the predictability of the future from the past in Gaussian stationary stochastic process. In this talk, we consider measures on the real line for which logarithmic integral exists and give their complete characterization in terms of the Hamiltonian in De Branges canonical system. This provides a generalization of the classical Szego theorem for polynomials orthogonal on the unit circle and complements the celebrated Krein-Wiener theorem in complex function theory. The applications to Krein strings and Gaussian processes with continuous time will be discussed (this talk is based on the joint paper with R. Bessonov).
Sun, 18/11/2018 - 12:00 to 13:00
Manchester building, room 209