King's College London

Quantitative results on continuity of the spectral factorization mapping in the scalar case

Research output: Working paperPre-print

Lasha Ephremidze, Eugene Shargorodsky, Ilya Spitkovsky

Original language English Published - 3 Mar 2016

Documents

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1603.01101v1, 147 KB, application/pdf

18/03/2016

Abstract

In the scalar case, the spectral factorization mapping $f\to f^+$ puts a nonnegative integrable function $f$ having an integrable logarithm in correspondence with an outer analytic function $f^+$ such that $f = |f^+|^2$ almost everywhere. The main question addressed here is to what extent $\|f^+ - g^+\|_{H_2}$ is controlled by $\|f-g\|_{L_1}$ and $\|\log f - \log g\|_{L_1}$.