Eugene Shargorodsky (KCL)

Quantitative results on continuity of the spectral factorisation mapping

Abstract:
It is well known that the matrix spectral factorisation mapping is continuous from the Lebesgue space L1 to the Hardy space H2 under the additional assumption of uniform integrability of the logarithms of the spectral densities to be factorised (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.