Quantitative results on continuity of the spectral factorisation mapping

Eugene Shargorodsky, King's College London. Part of the analysis and applications seminar series.

It is well known that the matrix spectral factorisation mapping is continuous from the Lebesgue space L^1 to the Hardy space H^2 under the additional assumption of uniform integrability of the logarithms of the spectral densities to be factorized (S. Barclay; G. Janashia, E. Lagvilava, and L. Ephremidze). The talk will report on a joint project with Lasha Epremidze and Ilya Spitkovsky, which aims at obtaining quantitative results characterising this continuity.