• Dirichlet Approximation and Universal Dirichlet 

      [OWP-2016-12] Aron, Richard M.; Bayart, Frédéric; Gauthier, Paul Montpetit; Maestre, Manuel; Nestoridis, Vassili (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] Falcó, Javier; Gauthier, Paul Montpetit; Manolaki, Myrto; Nestoridis, Vassili (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.
    • Hutchinson's Intervals and Entire Functions from the Laguerre-Pólya Class 

      [OWP-2022-19] Nguyen, Thu Hien; Vishnyakova, Anna (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-12)
      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}{ ...
    • The Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree One 

      [OWP-2017-03] Luce, Robert; Sète, Olivier (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] Gauthier, Paul Montpetit (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] Anderson, J. M.; Hinkkanen, Aimo (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] Moschonas, Dionysios; Nestoridis, Vassili (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-21)
      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 ...
    • Rational Approximation on Products of Planar Domains 

      [OWP-2016-05] Aron, Richard M.; Gauthier, Paul Montpetit; Maestre, Manuel; Nestoridis, Vassili; Falcó, Javier (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 ...
    • Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces 

      [OWP-2011-38] Si, Duc Quang (Mathematisches Forschungsinstitut Oberwolfach, 2011)
      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 ...
    • Solid extensions of the Cesàro operator on the Hardy space H2(D) 

      [OWP-2013-11] Curbera, Guillermo P.; Ricker, Werner J. (Mathematisches Forschungsinstitut Oberwolfach, 2013-04-23)
      We introduce and study the largest Banach space of analytic functions on the unit disc which is solid for the coefficient-wise order and to which the classical Ces`aro operator $\mathcal{C}:H^2 \to H^2$ can be continuously ...
    • Spherical Arc-Length as a Global Conformal Parameter for Analytic Curves in the Riemann Sphere 

      [OWP-2016-21] Gauthier, Paul Montpetit; Nestoridis, Vassili; Papadopoulos, Athanase (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 ...