Analytic approximation of rational matrix functions
| dc.creator | Peller, V. V. | |
| dc.creator | Vasyunin, V. I. | |
| dc.date | 2006-07-27 | |
| dc.date.accessioned | 2026-07-07T07:21:03Z | |
| dc.date.available | 2026-07-07T07:21:03Z | |
| dc.description | For a rational matrix function $Φ$ with poles outside the unit circle, we estimate the degree of the unique superoptimal approximation $\AΦ$ by matrix functions analytic in the unit disk. We obtain sharp estimates in the case of $2\times2$ matrix functions. It turns out that ``generically'' $°\AΦ\le\degΦ-2$. We prove that for an arbitrary $2\times2$ rational function $Φ$, $°\AΦ\le2\degΦ-3$ whenever $\degΦ\ge2$. On the other hand, for $k\ge2$, we construct a $2\times2$ matrix function $Φ$, for which $\degΦ=k$, while $°\AΦ=2k-3$. Moreover, we conduct a detailed analysis of the situation when the inequality $°\AΦ\le\degΦ-2$ can violate and obtain best possible results. | |
| dc.identifier | https://arxiv.org/abs/math/0607711 | |
| dc.identifier | http://arxiv.org/abs/math/0607711 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115168 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 47B35 | |
| dc.title | Analytic approximation of rational matrix functions | |
| dc.type | text |