Related papers: The corona problem with two pieces of data

In this note we solve that the corona problem for strongly pseudoconvex domains under a certain assumption on the level sets of the corona data.

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

The corona problem was motivated by the question of the density of the open unit disc in the maximal ideal space of the algebra of bounded holomorphic functions on the unit disc. The corona problem connects operator theory, function theory,…

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 $\mathbb{C}^n$.

We prove that the $\mathcal{H}^p$-corona problem has a solution for convex domains of finite type in $\mathbb{C}^n$, $n \ge 2$.

We prove an $H^2-$Corona theorem with estimate $C(\delta)=C\delta^{-1-q}|\log \delta|$ for $\delta\ll 1$ on delta-regular domains, where $q=\min\{n,m-1\}$ and $m$ is the number of generators. This class of domains includes smooth bounded…

Let $E$ be a Banach lattice on $\mathbb Z$ having order continuous norm. We show that for any function $f = \{f_j\}_{j \in \mathbb Z}$ from the Hardy space $H_\infty (E)$ such that $\delta \leqslant \|f (z)\|_E \leqslant 1$ for all $z$ from…

In this note we show that if the Corona data depends continuously (smoothly) on a parameter, the solutions of the corresponding Bezout equations can be chosen to have the same smoothness in the parameter.

We prove the corona theorem for domains whose boundary lies in certain smooth quasicircles. These curves, which are not necessarily Dini-smooth, are defined by quasiconformal mappings whose complex dilatation verifies certain conditions.…

The goal of this note is to present a simple mathematical model with two parameters for the number of deaths due to the corona (COVID-19) virus. The model only requires basic knowledge in differential calculus, and can also be understood by…

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…

Let $K$ be a square Cantor set, i.e. the Cartesian product $K=E\times E$ of two linear Cantor sets. Let $\delta_n$ denote the proportion of the intervals removed in the $n$th stage of the construction of $E$. It is shown that if…

The paper focuses on studying strong geodetic sets and numbers in the context of corona-type products of graphs. Our primary focus is on three variations of the corona products: the generalized corona, generalized edge corona, and…

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…

We discuss domains of holomorphy and several notions of pseudoconvexity (drawing parallels with the corresponding notions from geometric convexity), and present a mostly self-contained solution to the Levi problem. We restrict our attention…

We propose a simple model for understanding the kinetics of corona virus transmission. Our model assume spreading of corona virus can happen from one to another only, if someone without enough protection comes close contact to a person…

We investigate the 2-center problem for arbitrary strictly convex, centrally symmetric curves instead of usual circles. In other words, we extend the 2-center problem (from the Euclidean plane) to strictly convex normed planes, since any…

We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.

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…

We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the $K$-homology of the corona with the $K$-theory of the Roe algebra, via the coarse assembly map. We also…