Can I read Toeplitz condition numbers as an $H^{\infty}$ interpolation problem on EtoBox?

Toeplitz condition numbers as an $H^{\infty}$ interpolation problem by Zarouf, Rachid is a scholarly article available to read on EtoBox.

What is Toeplitz condition numbers as an $H^{\infty}$ interpolation problem about?

The condition numbers $CN(T)==||T|| .||T^{-1}|| $ of Toeplitz and analytic $n\times n$ matrices $T$ are studied. It is shown that the supremum of $CN(T)$ over all such matrices with $||T|| \leq1$ and the given minimum of eigenvalues $r=min_{i=1..n}|\lambda_{i}|>0$ behaves as the corresponding supremum over all $n\times n$ matrices (i.e., as $\frac{1}{r{}^{n}}$ (Kronecker)), and this equivalence is uniform in $n$ and $r$. The proof is based on a use of the Sarason-Sz.Nagy-Foias commutant lifting theorem.

Author

Zarouf, Rachid

Published

2011

Language

EN