Related papers: A new proof of the corona problem

The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with…

This paper addresses the Corona problem for slice hyperholomorphic functions for a single quaternionic variable. While the Corona problem is well-understood in the context of one complex variable, it remains highly challenging in the case…

Let $H^\infty(\Delta)$ be the uniform algebra of bounded analytic functions on the open unit disc $\Delta$, and let $\mathfrak{M}(H^\infty)$ be the maximal ideal space of $H^\infty(\Delta)$. By regarding $\Delta$ as an open subset of…

For a wide class of domains $G\subset\mathbb C^d$ including balls and polydisks we prove the density of their canonical image in the spectrum of $H^\infty(G)$. This Corona Theorem is proved first in its abstract version for certain uniform…

We study the corona problem on the unit ball in $\CC^n$, and more generally on strongly pseudoconvex domains in $\CC^n$. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able…

We obtain estimates in the corona theorem for the algebra of analytic functions in the unit disc whose nth derivative is bounded, and its subalgebras defined by the boundary continuity of the nth derivative. The corona theorem for such…

Let $B$ be a Blaschke product. We prove in several different ways the corona theorem for the algebra $H^\infty_B:=\mC+BH^\infty$. That is, we show the equivalence of the classical {\em corona condition} on data $f_1, ..., f_n \in…

We prove an alternate Toeplitz corona theorem for the algebras of pointwise kernel multipliers of Besov-Sobolev spaces on the unit ball in $\mathbb{C}^{n}$, and for the algebra of bounded analytic functions on certain strictly pseudoconvex…

The main goal of this paper is to give an unified proof of the corona problem on weighted Hardy spaces and on Morrey spaces. We use a technique that allows to reduce the problem to the Hardy spaces $H^2(\theta)$

The main purpose of this paper is to extend and refine some work of Agler-McCarthy and Amar concerning the Corona problem for the polydisk and the unit ball in $\mathbb{C}^n$.

In this paper, we obtain estimates for the solutions to the classical B{\'e}zout equation that are analogous to Carleson's solution to the corona theorem for the bounded analytic functions on the open unit disk. As an application, we extend…

This paper proves a corona theorem for the algebra of Radon measures compactly supported in $\mathbb{R}_-$ and this result is applied to provide a necessary and sufficient Hautus--type frequency criterion for the $L^1$ exact controllability…

The main result of the paper is the theorem giving a sufficient condition for the existence of a bounded analytic projection onto a holomorphic family of (generally infinite-dimensional) subspaces (a holomorphic sub-bundle of a trivial…

This paper utilizes Cauchy's transform and duality for the Dirichlet-type space $D(\mu)$ with positive superharmonic weight $U_\mu$ on the unit disk $\mathbb{D}$ to establish the corona theorem for the Dirichlet-type multiplier algebra…

The matrix-valued {Bezout-corona} problem $G(z)X(z)=I_m$, $|z|<1$, is studied in a Wiener space setting, that is, the given function $G$ is an analytic matrix function on the unit {disc} whose Taylor coefficients are absolutely summable and…

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems,…

Carleson's corona theorem is used to obtain two results on cyclicity of singular inner functions in weighted Bergman-type spaces on the unit disk. Our method proof requires no regularity conditions on the weights.

We find a formula for the area of disks tangent to a given disk in an Apollonian disk packing (corona) in terms of a certain novel arithmetic Zeta function. The idea is based on "tangency spinors" defined for pairs of tangent disks.

We establish an equivalency of the Corona problem (1962) and Gleason problem (1964) in the theory of several complex variables. As an application, we give an affirmative solution of the Corona problem for certain bounded pseudoconvex…

We study the corona problem on the unit ball and the unit polydisc in $\CC^n$. We provide affirmative solutions to both problems.