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arXiv · 1603.01101

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

Lasha Ephremidze·Eugene Shargorodsky·Ilya Spitkovsky
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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 $\|\log f - \log g\|_{L_1}$.

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Lasha Ephremidze, Eugene Shargorodsky, Ilya Spitkovsky. 2016-03-03. Quantitative results on continuity of the spectral factorization mapping in the scalar case. https://doi.org/10.1007/s40590-016-0117-7

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