A Note about Stabilization in $A_\R(\D)$

Details A Note about Stabilization in $A_\R(\D)$ A Note about Stabilization in $A_\R(\D)$

2007-01-31

arxiv.org/abs/math/0702003v1

Math. Nachr. 282 (2009), no. 6, 912--916

Mathematics

Classical Analysis and ODEs

5 pages, to appear in Math. Nachr

Scientific paper

10.1002/mana.200610779

It is shown that for $A_\R(\D)$ functions $f_1$ and $f_2$ with $$ \inf_{z\in\bar{\D}}(\abs{f_1(z)}+\abs{f_2(z)})\geq\delta>0 $$ and $f_1$ being positive on real zeros of $f_2$ then there exists $A_\R(\D)$ functions $g_2$ and $g_1,g_1^{-1}$ with and $$ g_1f_1+g_2f_2=1\quad\forall z\in\bar{\D}. $$ This result is connected to the computation of the stable rank of the algebra $A_\R(\D)$ and to Control Theory.

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