We characterize the uniform limits of Dirichlet polynomials on a right half plane. We extend the approximation theorems of Runge, Mergelyan and Vitushkin to the Dirichlet setting with respect to the Euclidean distance and ...

We find the intervals $[\alpha, \beta (\alpha)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots$ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{ ...

For an analytic curve $\gamma : (a,b) \to \mathbb{C}$, the set of values approaches by $\gamma(t)$, as $t ↘a$ and as $t↗b$ can be any two continuua of $\mathbb{C} \cup \{\infty\}$.

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 ...

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove ...

We prove that for every analytic curve in the complex plane $\mathbb{C}$, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic ...