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

Lasha Ephremidze; Eugene Shargorodsky; Ilya Spitkovsky

doi:10.1007/s40590-016-0117-7

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 $\|\log f - \log g\|_{L_1}$.

Original language	English
Pages (from-to)	517-527
Number of pages	11
Journal	Boletín de la Sociedad Matemática Mexicana
Volume	22
Issue number	2
Early online date	8 Apr 2016
DOIs	https://doi.org/10.1007/s40590-016-0117-7
Publication status	Published - Oct 2016

Keywords

Spectral factorization, Paley–Wiener condition, Convergence rate

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10.1007/s40590-016-0117-7Licence: CC BY

Quantitative results on continuity_EPHREMIDZE_Accepted26February2016_GOLD VoR (CC BY)Final published version, 589 KBLicence: CC BY

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AU - Spitkovsky, Ilya

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ER -

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

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