Dirichlet approximation and universal Dirichlet series

We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series.

Extendability and domains of holomorphy in infinite-dimensional spaces

A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables

For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.

A Note on the Density of Rational Functions in A ∞(Ω)

We present a sufficient condition to ensure the density of the set of rational functions with prescribed poles in the algebra A ∞ (Ω).