Related papers: T-universal Functions With Prescribed Approximatio…

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…

A compact subset $K$ of the complex plane $\C$ is a set of polynomial (respectively rational) approximation if $P(K)=A(K)$ (respectively $R(K)=A(K)$), where $P(K)$ (respectively $R(K)$) is the family of functions on $K$ which are uniform…

We prove simultaneous Universal Approximation of a certain type of Pade Approximants and of Taylor series with the same indexes. This is a generic phenomenon in the space of holomorphic functions in any simply connected domain, as well as…

New sufficient conditions, concerned with the coefficients of harmonic functions $f(z)=h(z)+\bar{g(z)}$ in the open unit disk $\mathbb{U}$ normalized by $f(0)=h(0)=h'(0)-1=0$, for $f(z)$ to be harmonic close-to-convex functions are…

Consider the family of locally univalent analytic functions $h$ in the unit disk $|z|<1$ with the normalization $h(0)=0$, $h'(0)=1$ and satisfying the condition $${\real} \left( \frac{z h''(z)}{\alpha h'(z)}\right) <\frac{1}{2} ~\mbox{ for…

Let $X$ be a smooth, projective, geometrically connected curve over a finite field $\mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Its dual group $\hat{G}$ is a split reductive group over $\mathbb{Z}$.…

Given a finite set \sigma of the unit disc \mathbb{D}=\{z\in\mathbb{C}:,\,| z|<1\} and a holomorphic function f in \mathbb{D} which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes…

This paper studies the determining sets for analytic functions from the symmetrized bidisk into the open unit disk in $\mathbb C$. It relates the idea to the uniqueness of the solutions of a Nevanlinna-Pick interpolation problem. It also…

We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the…

We study locally univalent functions $f$ analytic in the unit disc $\mathbb{D}$ of the complex plane such that $|{f"(z)/f'(z)}|(1-|z|^2)\leq 1+C(1-|z|)$ holds for all $z\in\mathbb{D}$, for some $0<C<\infty$. If $C\leq 1$, then $f$ is…

Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in…

In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call $F$-harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral…

Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline…

We establish that the Grunsky norm of any normalized univalent function on the disk is completely determined by the squares of holomorphic abelian differentials (in contrast to the Teichmuller norm, which relates to all integrable…

A starlike univalent function $f$ is characterized by the function $zf'(z)/f(z)$; several subclasses of these functions were studied in the past by restricting the function $zf'(z)/f(z)$ to take values in a region $\Omega$ on the right-half…

In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it…

We call a function $f$ in $C(X)$ to be hard-bounded if $f$ is bounded on every hard subset, a special kind of closed subset, of $X$. We call a subset $T$ of $X$ to be $S$-embedded if every hard-bounded continuous function of $T$ can be…

We describe the norming sets for the space of global holomorphic sections to a $k$-power of a positive holomorphic line bundle on a compact complex manifold $X$. We characterize in metric terms the sequence of measurable subsets…

Let ${\rm {\mathbb G}}$ be a domain with closed rectifiable Jordan curve $\ell $ . Let $K({\rm {\mathbb G}})$ be the space of all analytic functions in ${\rm {\mathbb G}} $ representable by a Cauchy - Stieltjes integral. Let ${\rm…

We consider the spaces $H_{F}^{\infty}(\Omega)$ and $\mathcal{A}_{F}(\Omega)$ containing all holomorphic functions $f$ on an open set $\Omega \subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq \mathbb{N}_0=\{…