Related papers: Another proof of the corona theorem

In this paper we prove that every collection of measurable functions $f_\alpha$, $|\alpha|=m$ coincides a.e. with $m$th order derivatives of a function $g\in C^{m-1}$ whose derivatives of order $m-1$ may have any modulus of continuity…

Let $P_{2k}$ be a homogeneous polynomial of degree $2k$ and assume that there exist $C>0$, $D>0$ and $\alpha \ge 0$ such that \begin{equation*} \left\langle P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left(…

Let $b$ be a nonextreme function in the unit ball of $H^{\infty}$ on the unit disk $\mathbb{D} $ and let $a$ be an outer $H^{\infty}$ function such that $|a|^2+|b|^2=1$ almost everywhere on $\partial \mathbb{D}$. The sufficient and…

Let A be an introverted algebra with mean value. We prove that its spectrum \Delta (A) is a compact topological semigroup, and that the kernel K(\Delta (A)) of \Delta (A) is a compact topological group over which the mean value on A can be…

In this paper we continue our research of functions on the boundary of their domain and obtain some results on cluster sets of functions between topological spaces. In particular, we prove that for a metrizable topological space $X$, a…

For some special window functions $\psi_{\beta} \in H^2(\mathbb{C}^+),$ we prove that, over all sets $\Delta \subset \mathbb{C}^+$ of fixed hyperbolic measure $\nu(\Delta),$ the ones over which the Wavelet transform…

We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $\tau^*$ of the natural topology of the real line $\mathbb{R}$ with properties such…

The notion of a quasi-free Hilbert module over a function algebra $\mathcal{A}$ consisting of holomorphic functions on a bounded domain $\Omega$ in complex $m$ space is introduced. It is shown that quasi-free Hilbert modules correspond to…

Let $\Omega\subset\mathbb{C}$ be a bounded domain such that there exists an algebraic harmonic function of degree two vanishing on the boundary of $\Omega.$ Then we show that the Khavinson-Shapiro conjecture holds for $\Omega:$ if the…

Let $\Omega \Subset \mathbb C^n$ be a bounded strongly $m$-pseudoconvex domain ($1\leq m\leq n$) and $\mu$ a positive Borel measure with finite mass on $\Omega$. Then we solve the H\"older continuous subsolution problem for the complex…

We continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\mathbb C^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the…

The different dynamical processes (relaxation, dynamical friction, tides and mergers) operating in groups and clusters are reviewed. The small-scale substructure observed in clusters is argued to be the remnants of the cores of rich…

On bounded B-regular domains, we study envelopes of plurisubharmonic functions bounded from above by a function $\phi$ such that $\phi^*=\phi_*$ on the closure of the domain. For $\phi$ satisfying certain additional criteria limiting its…

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable $C^*$-algebras with the metric approximation property…

Let $\Omega$ be an open set with Ahlfors-David regular boundary satisfying the corkscrew condition. When $\Omega$ is connected in some quantitative form one can establish that for any real elliptic operator with bounded coefficients, the…

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family.…

In the context of continuous zooming systems $f:M \to M$ on a compact metric space $M$, which include the non-uniformly expanding ones, possibly with the presence of a critical set, with the zooming set dense in $M$, we prove that any…

The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start…

We show that under minimal assumptions on a class of functions $\mathcal{H}$ defined on a probability space $(\mathcal{X},\mu)$, there is a threshold $\Delta_0$ satisfying the following: for every $\Delta\geq\Delta_0$, with probability at…