Year: 2020
Type: preprint
Abstract: Let $H^\infty(\mathbb D\times\N)$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk $\mathbb D\subset\mathbb C$. We show that the dense stable rank of $H^\infty(\mathbb D\times\N)$ is one and using this fact prove some nonlinear Runge-type approximation theorems for $H^\infty(\mathbb D\times\N)$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for algebra $H^\infty(\mathbb D)$.
Source: arXiv (Cornell University)
Author: Brudnyi, Alexander
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3033739598