@article{Nikolski_2017, title={Bounding smooth solutions of Bezout equations}, volume={121}, url={https://www.mscand.dk/article/view/26387}, DOI={10.7146/math.scand.a-26387}, abstractNote={<p>Given data $f=(f_1,f_2,\dots ,f_n)$ in the holomorphic part $ A= F_+$ of a symmetric Banach\slash topological algebra $ F$ on the unit circle $\mathbb{T}$, we estimate solutions $ g_j\in A$ to the corresponding Bezout equation $\sum _{j=1}^ng_jf_j=1$ in terms of the lower spectral parameter δ, $0&lt; \delta \leq |f(z)|$, and an inversion controlling function $c_1(\delta ,F)$ for the algebra $F$. A scheme developed issues from an analysis of the famous Uchiyama-Wolff proof to the Carleson corona theorem and includes examples of algebras of “smooth” functions, as Beurling-Sobolev, Lipschitz, or Wiener-Dirichlet algebras. There is no real “corona problem” in this setting, the issue is in the growth rate of the upper bound for $\|g\|_{A^n}$ as $\delta \to 0$ and in numerical values of the quantities that occur, which are determined as accurately as possible.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Nikolski, Nikolai}, year={2017}, month={Sep.}, pages={121–143} }