# 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.