Quantitative results on continuity of the spectral factorization mapping

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 $F=F^{+}(F^{+}{)}^{\ast }$ almost everywhere. The main question addressed here is to what extent $\Vert F^{+}-G^{+}{\Vert }_{H_2}$ is controlled by $\Vert F-G{\Vert }_{L_1}$ and $\Vert \log \det F-\log \det G{\Vert }_{L_1}$.

22 pages

References in corpus (1)

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

Cited by in corpus (1)

• The Spectral Approach to Linear Rational Expectations Models