Now showing items 1-10 of 10

• #### 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 Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree One ﻿

[OWP-2017-03] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-02)
We study harmonic mappings of the form $f(z) = h(z) - \overline{z}$, where $h$ is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the ...
• #### 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 $\mathbb{C} \cup \{\infty\}$.
• #### A new counting function for the zeros of holomorphic curves ﻿

[OWP-2009-25] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-18)
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the ...
• #### Non-Extendability of Holomorphic Functions with Bounded or Continuously Extendable Derivatives ﻿

[OWP-2017-30] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-21)