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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the scalar case, the spectral factorization mapping f → f⁺ puts a nonnegative integrable function f having an integrable logarithm in correspondence with an outer analytic function f⁺ such that f = |f⁺|² is almost everywhere. The main question addressed here is to what extent ||f⁺-g⁺||_H2 is controlled by || f-g ||_L1 and || log f - log g||_L1.

Original language	English (US)
Pages (from-to)	517-527
Number of pages	11
Journal	Boletin de la Sociedad Matematica Mexicana
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s40590-016-0117-7
State	Published - Oct 2016

Keywords

Convergence rate
Paley-Wiener condition
Spectral factorization

ASJC Scopus subject areas

General Mathematics

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10.1007/s40590-016-0117-7

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abstract = "In the scalar case, the spectral factorization mapping f → f+ puts a nonnegative integrable function f having an integrable logarithm in correspondence with an outer analytic function f+ such that f = |f+|2 is almost everywhere. The main question addressed here is to what extent ||f+-g+||H2 is controlled by || f-g ||L1 and || log f - log g||L1.",

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AU - Spitkovsky, Ilya

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KW - Convergence rate

KW - Paley-Wiener condition

KW - Spectral factorization

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

Abstract

Keywords

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