Quantitative results on continuity of the spectral factorization mapping

L. Ephremidze; E. Shargorodsky; I. Spitkovsky

doi:10.1112/jlms.12258

Quantitative results on continuity of the spectral factorization mapping

L. Ephremidze, E. Shargorodsky, I. Spitkovsky

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Abstract

The spectral factorization mapping $F\to F^+$ puts a positive definite integrable matrix function $F$ having an integrable logarithm of the determinant in correspondence with an outer analytic matrix function $F^+$ such that $F = F^+(F^+)^*$ almost everywhere. The main question addressed here is to what extent $\|F^+ - G^+\|_{H_2}$ is controlled by $\|F-G\|_{L_1}$ and $\|\log \det F - \log\det G\|_{L_1}$.

Original language	English
Pages (from-to)	60-81
Journal	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume	101
Issue number	1
Early online date	22 Jul 2019
DOIs	https://doi.org/10.1112/jlms.12258
Publication status	E-pub ahead of print - 22 Jul 2019

Keywords

30D99
46E30
46E40 (secondary)
47A68 (primary)

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10.1112/jlms.12258

Quantitative results_EPHREMIDZE_Accepted6thJulyAccepted author manuscript, 408 KBLicence: Other

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AU - Spitkovsky, I.

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KW - 30D99

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JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

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Quantitative results on continuity of the spectral factorization mapping

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Keywords

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