Now showing items 1-5 of 5

• #### Dirichlet Approximation and Universal Dirichlet ﻿

[OWP-2016-12] (Mathematisches Forschungsinstitut Oberwolfach, 2016-08-16)
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 ...
• #### A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables ﻿

[OWP-2019-02] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-11)
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.
• #### The Initial and Terminal Cluster Sets of an Analytic Curve ﻿

[OWP-2016-25] (Mathematisches Forschungsinstitut Oberwolfach, 2016-12-21)
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 $\mathbb{C} \cup \{\infty\}$.
• #### Rational Approximation on Products of Planar Domains ﻿

[OWP-2016-05] (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)
We consider $A(\Omega)$, the Banach space of functions $f$ from $\overline{\Omega}=\prod_{i \in I} \overline{U_i}$ to $\mathbb{C}$ that are continuous with respect to the product topology and separately holomorphic, where ...
• #### Spherical Arc-Length as a Global Conformal Parameter for Analytic Curves in the Riemann Sphere ﻿

[OWP-2016-21] (Mathematisches Forschungsinstitut Oberwolfach, 2016-11-11)
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 ...